Kinks in the angle resolved photoemission and inelastic x...

Kinks in the angle resolved photoemission and

inelastic x-ray spectra of high temperature

superconductors

Je Graf

May 22, 2008

A Thesis submitted for the degree of Doctor of Philosophy

School of Basic Sciences, Physics department.

Swiss Federal Institute of Technology

Chair :

Alessandra Lanzara, (University of California, Berkeley & LawrenceBerkeley National Laboratory)

Giorgio Margaritondo, (Swiss Federal Institute of Technology)

ii

Abstract

Though the high superconducting transition temperature (Tc) is the mostinteresting technological aspect of high temperature superconductors, thecomplex way in which the spin, lattice and electronic degrees of freedominterplay, makes them of the highest scientic interest. This is illustratedby their rich phase diagram characterized by a variety of exotic groundstateincluding; Mott insulating, pseudogap and high temperature superconduc-tivity.

One of the most serious barriers that has prevented our understandingof the mechanism of high temperature superconductors thus far is the lackof information on how low energy Landau quasiparticles result from an or-ganization of real particles. This organization, often colloquially referred toas dressing, is a fundamental general concept in physics that explains avariety of physical phenomena, such as exotic particle formations and phasetransitions.

The role of the lattice in this dressing is particularly controversial. Phononsare quanta of lattice vibration energy, and play a crucial role in conventionalsuperconductivity. They provide an attractive interaction allowing the elec-trons to condensate in superconducting Cooper pairs. However, high tem-perature superconductivity in the cuprates in achieved through hole dopingin an antiferromagnetic Mott insulator. In this case, the antiferromagneticbackground, the strong coulomb repulsion and the anisotropic superconduct-ing gap all suggest a marginal role of the phonons.

In order to assess experimentally the exact role of the phonon, angleresolved photoemission spectroscopy (ARPES) is the weapon of choice givenits unique ability to probe the electronic structure of solids in an energy- andmomentum-resolved manner. In this thesis, I will use ARPES to characterizethe various form of dressing of the quasiparticles in the high temperaturesuperconductor from the Fermi level all the way to the valence band complex.I'll show that when combined with isotope substitution and inelastic x-raysscattering, the strong electron-phonon interaction can be probed in vividdetails.

This thesis presents present three fundamental results. 1) Using the iso-tope eect, the important and unusual role of the phonon is demonstrated,as well as the strong interplay between the magnetic and phonic degrees offreedom. 2) Using inelastic scattering, the intriguing interplay between theFermi surface and the bond stretching phonon is exposed. And 3) By ex-ploring the ARPES data up to high energy, two new energy scales at highbinding energy as well as the spectral waterfalls phenomenon are revealed.

When all these new elements are considered together, they clearly showthe need to consider simultaneously the spin, lattice, Fermi surface topologyand electronic degrees of freedom.

The spectacular progress in ARPES techniques over the past two decadeswas critical for these results, and I will present in this thesis our current eortin pushing the techniques even further. In particular I'll present my eortsin building a laser based ARPES setup with a hemispherical analyzer and aspin resolved time of ight analyzer.

Keywords

ARPES, photoemission, IXS, inelastic scattering, cuprates, superconductiv-ity, kink, waterfalls, phonons, Fermi arcs.

iv

Résumé

Un des plus grands mystères de la supraconductivité à haute températureréside dans l'organisation des particules élémentaires en quasi-particules.De manière plus générale, ce concept de superposition est fondamental enphysique de la matière condensée. Il permet de comprendre et expliquer en-tre autres des transitions de phases ou des excitations électroniques exotiquesavec des charges fractionnelles.

Grâce à son unique potentiel à mesurer la structure électronique dessolides, la technique de photoémission résolue en angle (ARPES) permetd'étudier en détail ces excitations collectives, ou quasi-particules. De cefait, cette technique est rapidement devenue le fer de lance expérimental enphysique des matériaux complexes. La combinaison de cette technique avecla substitution d'isotope ou la diraction inélastique au rayon-X (IXS) per-met aujourd'hui d'étudier des modes collectifs spéciques tels que les phononsavec une résolution sans précédent.

Cette thèse est une étude des diérents types d'organisations électron-iques observés à diérents ordres d'énergie dans les cuprates supraconduc-teurs eectuée à l'aide de ces deux outils. Les principaux résultats sont : 1)le rôle intéressant and inhabituel des phonons sur la structure électroniqueet magnétique. 2) l'importance de la topologie de la surface de fermi pourl'interaction électron-phonon. 3) la présentation de deux nouveaux ordred'énergies dans le spectre ARPES. La synthèse de ces résultats indique aquel point il est important de considérer simultanément la charge, le spin etle réseau cristallins dans un model réaliste de la supraconductivité a hautetemperature.

Mots clés

photoémission, diraction inélastique, supraconductivité

vi

Dedication

To my family.

viii

Acknowledgment

I am much indebted to the excellent group of people that I have luckily comeinto contact with and beneted from in the course of this thesis work. Firstof all, my deep thanks go to Prof. Alessandra Lanzara, my advisor, whoset the topics, taught me, supported me and encouraged me throughout theprogram. Her enthusiasm was most inspiring.

I thank Prof. Gey-Hong Gweon, Prof. Kyle McElroy and Dr. AndreasSchmid for their collaboration and stimulating interaction. They patentlytaught me about superconductivity, correlated systems, photoemission, spinpolarized low energy electron microscopy and other philosophical matter ofrelevance.

Most of this work was done with the help of the past and present graduatestudent of the Lanzara group; Dr. Shuyun Zhou, Chris Jozwiak, DanielGarcia and David Siegel. With them I shared the pleasures of night and dayshifts, journal clubs, personal meetings and other daily trauma of a graduatestudent life. For making this experience such a pleasant one, I could not havefound better friends.

Throughout my thesis, I had the constant theoretical support from Prof.D.H. Lee. His deep physics insights and his enthusiasm for nding the mostbeautiful solutions are very inspiring. I thank him for his patience and forall the ideas he gave me.

I enjoyed working with Dr. Matteo d'Astuto on all the IXS runs at ESRFas well as the support and advices of Dr. M. Krisch at ESRF and Dr. A.Baron at SPring8.

A. Bostwick and A.V. Fedorov, E. Rotenberg, who generously sharedtheir expertise on photoemission at beamline 7, 10 and 12 to make the largepart of this thesis work possible.

I would like to thank Prof. Giorgio Margaritondo for making this workpossible, and his precious advices.

I would like to thank as well Z. Hussain, A. Bill, A. Bansil, A. Bianconi,R.S. Markiewicz, V. Oganesyan, P. Phillips, and S. Sahrakorpi for usefuldiscussions.

I thank T. Sasagawa, H. Eisaki, S. Uchida, H. Takagi for beautiful highTc samples and warm collaborative supports.

I'm very grateful my mother and my sister for letting me travel a longway from home and visiting me. They have encouraged and supported methroughout all stages of my education, and for that I am forever grateful.

Especially, I thank my wife, Marine, for her patience when I was late atnight, her encouragements when I had to leave early in the morning and hersupport and enthusiasm when nothing was working. Her smile is by far themost important driving force behind this thesis.

Figure 1: Some of the usuals suspects in the Lanzara group.

x

Contents

1 Introduction 1

2 High-Tc superconductors 52.1 Electronic structure and phase diagram . . . . . . . . . . . . . 52.2 Gap anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Pseudogap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Electron-phonon interaction . . . . . . . . . . . . . . . . . . . 9

3 Experimental techniques 133.1 Angle resolved photoemission spectroscopy (ARPES) . . . . . 13

3.1.1 Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . 143.1.2 Three steps model . . . . . . . . . . . . . . . . . . . . 153.1.3 Sudden approximation . . . . . . . . . . . . . . . . . . 163.1.4 Distribution curves . . . . . . . . . . . . . . . . . . . . 18

3.2 Laser based ARPES . . . . . . . . . . . . . . . . . . . . . . . 193.2.1 Advantages & caveats . . . . . . . . . . . . . . . . . . 203.2.2 Experimental setup . . . . . . . . . . . . . . . . . . . . 243.2.3 Pump-probe ARPES . . . . . . . . . . . . . . . . . . . 243.2.4 Preliminary data . . . . . . . . . . . . . . . . . . . . . 25

3.3 Spin-resolved, time-of-ight ARPES . . . . . . . . . . . . . . . 263.3.1 High-eciency spin polarimeter . . . . . . . . . . . . . 27

3.4 Inelastic x-ray scattering from collective atom dynamics . . . . 343.4.1 Scattering kinematics . . . . . . . . . . . . . . . . . . . 343.4.2 Dierential cross-section . . . . . . . . . . . . . . . . . 37

4 The isotope eect 39

5 The bond stretching phonon dispersion 45

6 The spectral waterfalls 57

7 Conclusions 67

List of abbreviations 68

Bibliography 70

Curriculum Vitae 75

xii

Chapter 1

Introduction

The discovery of high temperature superconductivity in the cuprates by KarlMüller and Johannes Bednorz in 1986 [1] was immediately awarded by theNobel prize in 1987. This was no surprise since these simple copper oxidecompounds can, amongst other things, carry an electrical current with noresistivity at temperature up to ≈ 137K (-136C), which is exceptionallyhigh compared to the previous records of 7.2K and 9.3K obtained with thesimple metals, lead (Pb) and Niobium (Nb).

`

Figure 1.1: Like conventional superconductors, high temperature supercon-ductors expel magnetic elds (Meissner eect), allowing them to levitate ina magnetic eld. (right panel) Superconducting ribbons can carry as muchcurrent as copper cables with 100 times the cross-sectional area. [2, 3].

This discovery raised the tantalizing possibility of achieving superconduc-tivity at room temperature, which would be a true revolution with cheap elec-trical power, magnetically levitated high-speed trains or high performancegenerator for wind turbines [3]. However, 20 years later the race to un-derstanding the mechanism behind high-temperature superconductivity andpushing the transitions temperature Tc to higher and higher values is stillongoing.

Beside the potential revolutionary applications, high temperature super-

2 Introduction

conductors are extremely interesting in themselves. Despite a frustratinglysimple crystal structure, they are very remarkable in many ways and displaya very rich phase diagram (from anti-ferromagnetic insulator to anomalousFermi liquid via a still mysterious pseudogap phase...), which remains elusive22 years later. This intricate phase diagram is a direct consequence of themultiple orders or states competing in this system. This makes of the highTc's one of the greatest contemporary challenge of condensed matter physicsand original angles of approaches are needed to shine a new light on this longstanding puzzle.

Over the last two decades, a signicant improvement in energy and mo-mentum resolution allowed angle-resolved photoemission spectroscopy (ARPES)to probe not only the electronic band structure, but the subtle many bodyphysics that aects it as well, inuencing some of the most important ques-tions of modern physics [4]. Indeed, while many of the properties of solidscan be revealed through transport and thermodynamic measurements, trueinsight requires the direct probing of the fundamental electronic structure.The copper oxides superconductors (cuprates) are a direct witness of thisinstrumental revolution [5, 6].

The first chapter presents a short introduction to high temperature su-perconductivity, with a main focus on the aspects relevant to my results. I'llintroduce the phase diagram and the key elements of the electronic structureand give some historical and contextual perspectives on the role of electron-phonon interactions in the cuprates.

The second chapter describes the two experimental techniques: angleresolved photoemission spectroscopy (ARPES) and inelastic x-ray scatter-ing (IXS) used in this thesis. I will also shortly describe my contributionin building our own in-house setup at the Lawrence Berkeley National Lab-oratory with a Helium discharge lamp and a laser light source. Finally Iwill briey describe our on-going eorts in developing the next generation ofspin-resolved ARPES experiments.

The third chapter is based on my rst contribution, Ref. [7]. Thisletter published in Nature magazine describes the anomalous isotope eectobserved in the cuprate. It shows the important and unconventional roleof the lattice degrees of freedom in the electron dynamics of the cuprates.Specically, by performing the rst ARPES study on oxygen isotopically sub-stituted double layer Bi2212, we could directly uncover the way the electronicstructure is aected by the lattice.

The fourth chapter is based on Ref. [8] and [9]. These two letterspublished in Physical Review B and Physical Review Letter are a follow upof the isotope work, exploring in more detail this anomalous electron phononcoupling. We performed a detailed analysis of the phonon band structure

3

using inelastic x-rays scattering and compared it with the electronic bandstructure. This study revealed important aspect of the anomalous softeningof the bond stretching phonon and an interesting correlation between theelectron phonon interaction and the Fermi surface topology.

The fifth chapter is based on Ref. [10, 11]. The isotope work hinted atthe presence of a new energy scale at about 0.4 eV. These two letters pub-lished Physical Review Letter and Physica C explore this high energy regionof ARPES spectrum. We present the rst detailed study of this strikinganomaly that we called the waterfalls as a function of doping and chemicalcomposition. To conclude, we present a model that potentially explains ourobservation.

The conclusion is presented in chapter sixth.

4 Introduction

Chapter 2

High-Tc superconductors

In this chapter I will present a brief introduction on the key concepts di-rectly related to my results. The curious reader is encouraged to dig in theextremely vast literature on the topic and the recent high quality reviews[5, 6, 12, 13].

2.1 Electronic structure and phase diagram

Though there are many families of cuprate high temperature superconductors(HTSC) [14], they all share a similar structure and phase diagram. They areall made of CuO2 atomic planes sandwiched by so called block layers of otheroxides as illustrated in Fig. 2.1. The electronic and magnetic active partsare the CuO2 planes. Since the charge carriers can only hardly hop fromone plane to another, the HTSC can be considered to a certain extent as astack of Josephson junctions or even more simply as just a quasi-2D system(an example of the limitations of this approximation in term of ARPES isdescribed in this ref. [15]).

Without doping, the CuO2 planes form an antiferromagnetic lattice witha Neel temperature of about TN=400K. Each Cu has one hole in the 3d shell,but contrary to what one would naively expect when the highest occupiedband contains one electron per unit cell (half lled system), the CuO2 areinsulating due to the very large on site Coulomb repulsion. This a charac-teristic properties of a Mott insulator, which is dened as material in whichthe conductivity vanishes as temperature tends to zero, even though bandtheory would predict it to be metallic 1.

The ve 3d-orbitals of the copper are split by the crystal elds into four

1In the case of the cuprates, the close presence of the oxygen 2p valence band redenedthem as charge transfer insulators [16].

6 High-Tc superconductors

Figure 2.1: Layer structure of the cuprates. The electronic and magneticactive parts are the CuO2 plans. The CuO2 atomic plane are sandwiched byso insulating layer called block layers or charge reservoir, since they host thedopant oxygens. Variations include two (bi-), three (tri-layer) or more CuO2

plane between each block layer (or per unit cell). The maximum Tc of ≈130K is obtained for the tri-layers compound. [17]

lower energy orbitals that are fully occupied (xy, xz, yz and 3 z2-r2), andone highest energy orbital, x2-y2 half lled. since the energies of the Cu 3d-orbitals and O 2p-orbitals are close in energy, there is a strong hybridizationbetween them. As a result, the topmost energy level has both Cudx2−y2 andOpx,y character.

It was proposed by F.C. Zhang and T.M. Rice [18] that this topmostenergy level would form a singlet ground state. The propagation of thissinglet is then well described with an eective single band Hubbard model[19]. Within this framework, the conduction band predicted with LDA cal-culation is strongly renormalized in a heavier band, by many body eects.The strong antiferromagnetism observed in the parent insulating compoundis believed to play a key role in this mechanism, but it is still not clear howthis mechanism evolves with large doping when the anti-ferromagnetic uc-tuation becomes weaker. In an attempt to address these pending questions,the behavior of the low energy part of this renormalized band has been verywell studied but data for the high energy part are still missing and it is notclear how the dispersion evolves close to the Γ point at the Brillouin zone(BZ) center.

The phase diagram is shown in Fig. 2.3. For doping range beyond afew percent, the system leaves the antiferromagnetic insulating phase fora peculiar ground state called the pseudo-gap state. The superconducting

2.2 Gap anisotropy 7

Figure 2.2: Fermi surface of overdoped Pb-Bi2Sr2CaCu2O8+δ measured in thesuperconducting phase. Data were taken in the second BZ and symmetrizedaccording to the tetragonal symmetry. The white solid lines correspond to atight binding t [7]. Note the nite discontinuous Fermi surface with Fermiarcs and gapped regions near the BZ face. The right panel shows the tightbinding model of the CuO2 plane with the momentum distribution functionn(k) in yellow.

phase starts shortly after and the transition temperature rises monotonicallywith doping, reaching a maximum at about 16% doping, after which Tcdeclines to zero. The net eect is to form a superconducting dome whichextends from about 5% to 25% doping. `

2.2 Gap anisotropy

The superconducting state is fairly unconventional with a highly anisotropicgap instead of the s-wave gap characteristic of superconductivity in metals.This gap is characterized by maximum along the Cu-O bond direction andvanishes at an angle 45 relative to that maximum (Fig. 2.2). Since ARPESis the only technique capable of measuring the momentum dependence ofthe energy gap it played a key role in establishing the symmetry of the orderparameter in the high Tc superconductors [20].


`

Figure 2.3: Phase diagram: As the system is doped with holes, the long-rangeantiferromagnetism (AF) disappears and the insulating properties transforminto metallic ones and there is a high-Tc superconducting range. This rangeis normally divided into an underdoped (UD), an optimally doped (OPT)and an overdoped (OD) region.

2.3 Pseudogap

While a gap in the quasiparticle spectrum was expected in the superconduct-ing state, surprisingly a similar anisotropic gap is found above the supercon-ducting transition temperature (Tc) in the metallic phase for all underdopedcuprates, when the carrier concentration is low and electron-electron correla-tions are very strong (Fig. 2.3). In this peculiar phase, the low-energy elec-tronic excitations occupy disconnected segments of the Fermi surface knownas Fermi arcs (Fig. 2.2). The origin of this so called pseudogap (whichonly partially gaps the Fermi surface) remains one of the key mysteries inthe study of High Tc superconductors [21, 22]. For example, whether thepseudogap is necessary for superconductivity, if it is a remnant of supercon-ductivity surviving to high temperatures, or if it indicates a competing phaseof matter such as charge ordering that suppresses the superconductivity re-mains unknown.

The relation between the Fermi arcs, the pseudogap and the supercon-ducting gap is non-trivial and is still an ongoing debate. Nevertheless hereare some of the latest pieces added to the puzzle using ARPES.

1. A very similar anisotropic gap was discovered in the manganite familyusing ARPES, La1.2Sr1.8Mn2O7 [23]: a compound with strong electron

2.4 Electron-phonon interaction 9

correlations and a ferromagnetic/metallic ground state. While the man-ganites exhibit remarkable behaviors like colossal magneto resistivity[24] where there is a drastic change in the resistivity with an appliedmagnetic eld it has no superconducting state. A similar anisotropicgap was reported as well for La2xBaxCuO4 with x = 1/8 [25], which isa particular doping where the superconductivity is strongly suppressedas static spin and charge orders or stripes develop [26, 27].

2. Near the BZ zone face (Fig. 2.2), ARPES revealed that the missingelectronic states begin to ll in until the pseudogap transition temper-ature (T*) is reached, where the gap abruptly closes [28, 29].

3. Fermi arcs are found above Tc, but bellow T*. ARPES showed thatthe Fermi arcs lengths depend only on the ratio T/T*, where T* is thetemperature below which the pseudogap rst develops at a given holedoping. The arcs collapse linearly with T/T* and extrapolate to zeroextent as T→0 [29].

4. Bellow Tc, ARPES showed that a single-particle BCS-like gap opensnear the nodal region in underdoped Bi2Sr2CaCu2O8+δ[30, 31].

All these evidences seem to point out that the pseudogap or the missingelectronic states at the BZ face represents an energy scale associated with adierent mechanism that may or may not be related to superconductivity.The Fermi arcs temperature scaling seems to point toward a scenario wherethe pseudo-gap is a precursor to superconductivity, while the presence of aBCS-like gap only around the node seems to point out a strong dichotomybetween the pseudogap and the superconducting gap. All these experimentsshow however that the gap, bellow or above Tc, is not simply d-wave [30, 32,31, 33].

2.4 Electron-phonon interaction

It took almost half a century to come up with a theory (the BCS theory [34])to explain superconductivity in metals using phonons, so it is not so surpris-ing that there is today no agreement, even qualitatively, on the origin of thesuperconducting ground state in the cuprate high temperature superconduc-tor only twenty two years or so after their discovery. Although the searchfor superconductivity in the cuprates by A. K. Muller and J. Bednorz wasmotivated by their tendency to polaron formation and hence, strong electron- phonon coupling, the presence of a phonon driven superconductivity in thecuprates was soon challenged for the following reasons [35]:


1. Tc is too high for a phonon driven mechanism.

2. The isotope eect (change of Tc when the isotope of the oxygen is sub-stituted) is much smaller than expected for a phonon-mediated pairing.

3. Pair elds with d-wave symmetry are not favoured by phonons.

4. Properties such as resistivity are not explained by electron phonon in-teractions. In particular the linear resistivity temperature dependencein optimally doped samples suggests a weak electron phonon coupling.

5. All copper oxide superconductors show uctuating antiferromagneticorder, which strongly suggests that unconventional physics is involved.

6. The layered crystal structures of the copper oxides suggest that specialtwo-dimensional physics is important, whereas phonons in two dimen-sions are probably no dierent from those in three.

Though none of these arguments are watertight [35], they all suggest amarginal lattice contribution.

However, this view was challenged by the report of a renormalization atabout 60 meV of the quasiparticle band structure in all cuprates families by abosonic mode (kink) [36, 37, 38], which was identify as a phonons by Lanzaraet al. [38].

Figure 2.4: Ubiquity of a sudden change (kink) in the dispersion along thenodal direction for dierent samples and at dierent doping levels (adaptedfrom Ref. [38]).

2.4 Electron-phonon interaction 11

The presence of a kink in all the cuprates, including material where nomagnetic resonance are observed, bellow and above the superconducting tem-perature and for a wide doping range was crucial in identifying the nature ofthe bosonic mode, phonons (Fig. 2.4).

Following the work by by Lanzara et al. [38] many experimental groupshave focused on studying the renormalization eects at low binding energyin dierent families of cuprates. The electron-phonon interaction picture hasgained momentum over the past years due to the following reports:

1. Observation of an universal anomalous softening of the in-plane Cu-Obond stretching mode (A1g) observed by inelastic scattering [39, 40, 41];

2. Fano-like lineshape and an abrupt softening upon entering the super-conducting state of the B1g phonon (out-of-plane oxygen vibrations)[42, 43];

However, whether these renormalization eects are truly caused by electron- phonon coupling or other mechanisms, such as spin uctuations, are atplay is still highly controversial in the eld. Moreover, even within the el-phonon coupling scenario, there is still much controversy on the nature ofthe electron-phonon coupling (beyond a simple Migdal-Eliashberg picture),the contribution of the strong electron-electron interaction in the ARPESspectrum [44, 45], and the role of the lattice and the magnetic resonances inthe superconductivity mechanism.


Chapter 3

Experimental techniques

I had the chance to join the group of Professor Lanzara on virtually day 1.This was exciting because the rst task for me and another graduate studentwas to build a lab with a state of the art ARPES system starting from0. Our analysis chamber is now fully functional, equipped with a Heliumdischarge lamp and a 6eV laser as light sources combined with a SPECS150mm electron analyzer. The rst data will be soon published (ref. [9]),and an example of the data quality is shown in Fig. 3.2. I was involvedas well in the design, assembly and testing of a new type of spin and angleresolved electron analyzer based on time of ight and exchange scattering,which will soon produce its rst results.

During my thesis, I have mainly used ARPES, laser ARPES and IXS sincethey present the perfect combination to uncover electron-phonon interactionin a material. Indeed on one hand ARPES is today by far the most powerfulprobe to study the electronic structure, and the many body interactions incomplex materials. On the other hand, IXS is the only instrument capableof mapping the phonon dispersion in small samples over the whole Brillouinzone. The combination of these complementary techniques have allowed tocarry on the rst study of this kind in cuprates.

In this chapter, I'll introduce these techniques, as well as the apparatuswe used and developed.

3.1 Angle resolved photoemission spectroscopy

(ARPES)

Angle Resolved photoemission is a unique spectroscopic tool to probe subtlemany body eects in highly correlated system. Such a powerful techniquecombined with high quality (quasi-)two dimensional samples turned out to be

14 Experimental techniques

a very prolic alliance and gave rise to an impressive number of high qualitypublications. I'll introduce here only the basics required, but the reader isstrongly encouraged to follow-up on more general and accurate reading likeref. [4, 6]

3.1.1 Hamiltonian

The photoemission process referred to the photons electrons interactions inmatter, one usually excite a electron from an initial state below the Fermilevel EF to some nal state above the vacuum level level with a incidentphoton. A non-relativistic description of this process including the spin de-pendence can be made out of the Dirac equation. The Hamiltonian is givenby

H =1

2m

(p− e

cA)2

+ eφ− e~2mc

σ∇×A

+ie~4mc

E · p− e~4mc

σ(E × p) (3.1)

where the rst two terms are from the Schrödinger description, the thirdterm, proportional to σ∇ × A = σ · B with σ the spin of the electron,represents the interaction of the magnetic dipole with the magnetic eld.The fourth term is a relativistic correction to the energy and the nal term,proportional to σ(E × p), represents the spin orbit coupling.

However, at photon energies typical of the ultraviolet (UV) and soft x-ray range, the probability of spin-ip to spin-conserving transitions is of theorder 2 · 10−2 [46]. The spin orbit term, σ(E × p), can lead to observablespin-polarization eects both in the initial and nal states, but in the absenceof spin orbit coupling, and considering using linearly polarized incident light,the Schrödinger description represents an adequate description of the spin-conserving transitions. Thus from Fermi's Golden rule the dierential crosssection, dσ/dΩ from a initial state |ψi〉 to a nal state |ψf〉 is given by

dσ

dΩ(Ef , ~ω, kf ,A) ∝ ∑

i

|〈ψf |(A · p+ p ·A)|ψi〉|δ(Ei − Ef − ~w) (3.2)

where the δ function describes the energy conservation of the process. Mea-suring the kinetic energy of the electron in the nal state Ef and knowing theincident photon energy, ~ω, the experimenter can trace back to the bindingenergy of the electron in the initial state Ei. The diamagnetic term |A| which

3.1 Angle resolved photoemission spectroscopy (ARPES) 15

is always small in the linear optical regime can be neglected and noting that∇·A is non-zero only in the surface region, equation (2.2) is usually reducedto the simpler form

dσ

dΩ∝∑i

|〈ψf |(A · p)|ψi〉|δ(Ei − Ef − ~w) (3.3)

3.1.2 Three steps model

Although this is a commonly used approximation, ∇ ·A might become im-portant at the surface, where the electromagnetic elds may have a strongspatial dependence. This surface photoemission contribution can interferewith the bulk contribution. In order to account for this, a model in whichphoton absorption, electron removal, and electron detection are treated asa single coherent process must be used [47, 48]. In this case bulk, surface,and vacuum have to be included in the Hamiltonian. This approach is veryreliable for calculating photoemission intensities, and gives important infor-mation about matrix element eects, i.e., the dependence of the ARPESintensity on k, and on the incident photon energy and polarization. Forthe high Tc cuprates However, due to the complexity of the one-step model,photoemission data are usually discussed within the three-step model, which,although purely phenomenological, has proved to be rather successful [5]. Ne-glecting ∇·A, the three-step model allows one to simplify the photoemissionprocess in three steps: 1) the creation of a photohole in the solid which can bedescribe using a Green's function 2) transport of the photoemitted electronto the surface and 3) escape of the photoelectron into the vacuum.

The rst step can be conveniently described by introducing the greenfunction. The photo-intensity I(k, ω) is then proportional to the spectralfunction A(k, ω) :

I(k, ω) ∝ MA(k, ω)f(ω)

where M is a matrix element and f(ω) is the Fermi function.The spectral function is the imaginary part of the Green's functionG(k, ω)

A(k, ω) = − 1

πImG(k, ω)

and by substituting, The spectral function can in turn be related to theelectron self-energy Σ(ω):

A(k, ω) =−1

π

Im(Σ(ω))

(ω − ε(k)−Re(Σ(ω)))2 + Im(Σ(ω))2


Where ε(k) is the non-interacting (bare) electron dispersion. In this form,it is easy to see how the imaginary part is related to the photohole lifetime(width of the peak) and the real part is related to the mass renormalizationand induces energy shifts of the peaks in the spectrum. The various manybody renormalizations of the bare dispersion can arise, in principle, from ei-ther electron-phonon or electron-electron interactions if the sudden approx-imation holds. However, these self-energy eects are impossible to evaluatein any controlled calculation. Nevertheless, they are useful in obtaining aqualitative understanding of the the various processes and estimating theirrelative importance.

3.1.3 Sudden approximation

However, using this formalisms requires that the outgoing photo-electron ismoving so fast that it has no time to interact with the photo-hole. Usingthis approximation (the sudden approximation), the photoemission processis assumed to be sudden, with no post-collisional interaction between thephotoelectron and the system left behind. With a back of the envelopecalculation, I will show that it is a fair approximation down to 15-30 eV [6].

The time spent by the escaping photoelectron in the vicinity of the photo-hole is the time available for their interaction. A photoelectron with a kineticenergy of 20 eV has a velocity v = 3× 108 cm/s. The relevant length scale,which is the smaller of the screening radius (of the photohole) and the escapedepth, is ≈ 10Å. Thus t = 3× 10−16 s, which should be compared with thetime scale for electron-electron interactions (which are the dominant sourceof interactions at the high energies of interest): tee = (2π)/ωp = 4× 10−15 s,using a plasma frequency ωp = 1 eV for the cuprates. If t tEE, then we cansafely ignore the interaction. From our very crude estimate t/tee = 0.1, sothat the situation with regard to the validity of the sudden approximation isnot hopeless. Fortunately, experimental checks have shown that indeed it wasa valid approximation. However in the case of laser ARPES, where electronkinetic energy are in the order of 2 eV, the validity of this approximation isclearly challenge, and it is surprising that most of the results still holds forthe high Tc [49].

For the second and third step, we can use conservation laws. In the solidstate momentum conservation is maintained through the mediation of thecrystal momentum giving

kf = ki +G

where ki and kf are the wave-vectors associated with the initial and nalstates and G represents a suitable lattice vector. To within a reciprocal

3.1 Angle resolved photoemission spectroscopy (ARPES) 17

Figure 3.1: Typical two dimensional ARPES data and the analysis of EDCsand MDCs.

Figure 3.2: Map of the band structure of TiTe2: Modern hemispherical elec-tron analyzer are equipped with 2D detector, with an energy and angle axis.By combining these energy-momentum slices for dierent angles, we can re-constructed the full electronic structure across the BZ, and ultimately mea-sure the Fermi surface.

lattice vector the parallel momentum k|| of the photo-electron given by

k|| =

(2m

~

)E1/2 sin θ


is conserved on crossing from the solid into the vacuum. Thus a measurementof this component in the vacuum supplies a good measure of the parallelcomponent in the solid. In addition, the conservation of energy relates thephotoelectron kinetic energy to the binding energy of the photohole in thecrystal through:

Ekin = hν − φ− |EB|where φ is the crystal work function.So, extending the technique and measuring the photo-emitted current

at some well dened angle it becomes possible to map the dispersion ofthe dierent initial-state bands. This is illustrated in the typical energy-momentum intensity map of Fig. 3.1. The combination of these 2D maps atdierent angles allow us to ultimately determine the Fermi surface as shownin Fig. 3.2.

3.1.4 Distribution curves

There are two ways to analyze the data. One way is to x momentum at aparticular value, and study intensity as a function of energy - energy distri-bution curves (EDCs). Another way is to x energy at a particular value,and study intensity as a function of momentum - momentum distributioncurves (MDCs). Each of these two methods has its own advantages anddisadvantages, and the analysis of these two is complimentary to each other.

EDC gives a global overview of the spectral function and the line shape.It provides information about whether a well-dened quasiparticle peak ispresent or not. Moreover, subtle features such as small peaks at low bindingenergy, presence of energy gaps[20] and more complicate lineshape (e.g. peak-dip-hump structure) due to self energy interaction can be observed clearly[5]. However, the line shape of the EDCs are usually complex and there isno unique theory to model them.

The MDC analysis is much simpler. MDC eliminates the eect of theFermi function and the energy dependent background. More importantly,the lineshape of MDC can usually be tted with a Lorentzian under the as-somption that the matrix element and the self energy vary smoothly withmomentum. Then, the peak positions from the MDC t gives direct informa-tion about the renormalized band dispersion and the MDC width is directlyrelated to the imaginary part of the self energy.

For my thesis, I collected most of the ARPES data at beamlines 7.0.1,10.0.1 and 12.0.1 of the Advanced Light Source in Berkeley and beamlineV-4 of the Stanford synchrotron radiation laboratory. The laser data were

3.2 Laser based ARPES 19

Figure 3.3: In-house ARPES chamber equipped with a SPECS He dischargelamp and 150mm analyzer

collected in the analysis chamber designed and built in our lab by me andmy colleague Chris Jozwiak, who is about to graduate as well. Fig 3.3show a recent picture of our apparatus. Note that the analyzer we usedis not a common Scienta analyser, but was manufactured by SPECS GmbH(http://www.specs.de/). This model is actually one of the rst one produced.After a long phase of testing and debugging of this new analyser, the rstdata are about to be published in physical review letter [8]. The TiTe2 datashown in Fig 3.2 were taken with this apparatus as well, but using the Hedischarge lamp (21.2eV)

3.2 Laser based ARPES

In the last part of my thesis I have been the main player behind the devel-opment of a laser based ARPES setup in the group of Prof. Lanzara. Thesystem is now fully functional and some of the data taken with this systemare included in ref. [8] (chapter 5). In this chapter, I'll introduce the ex-


perimental setup and the laser-ARPES technique with its advantages anddisadvantages.

Improvements in electron spectrometer technology over the past decadehave made it possible not only to measure the band structure and Fermisurface topology, but to observe ne structure in both the real and imaginaryparts of the electron self-energy which can be directly measured with AngleResolved Photoemission (ARPES). These technological breakthroughs havehad a major impact on condensed matter physics and in particularly on thecopper oxides superconductors (cuprates) [5]. For instance, the discoveriesof the D-wave symmetry of the superconducting order parameter [20] or ofthe key role of phonons in high temperature superconductor [38, 7] are directconsequences of these improvements.

However, ARPES is somewhat limited by the need of a high quality, exi-ble light source as provided by third generation synchrotron. Discharge lampsusing generally the HeI or HeII lines have been a widely used alternative inthe UV regime, despite their inherent limitations which we will not discusshere. However, the recent adoption of lasers as a complementary alternativelight source present now a very large potential gain in the ARPES arsenal.

3.2.1 Advantages & caveats

The main advantages of a laser based ARPES system are the following:

• the low photon energy (much lower than what most of the synchrotronbased sources can achieve) will allow for an increase of the bulk sensi-tivity (Fig. 3.4) and momentum resolution by about one order of mag-nitude with a much superior photon ux (1014 to 1015 photons/second).Note that in this case, the absence of the monochromator allow for avery high ux independently of the bandwidth.

• The low kinetic energy limit the total emission current, allowing to op-erate at intensity regimes not allowed at higher photon energy becauseof the space charging problem linked to the high number of secondaryphotoelectrons [51].

• The short pulse nature of the laser will allow table top pump-probeARPES experiments, opening the access to a dynamic view of the elec-tronic excitations in solids. In addition, repetition rates of the order ofthe MHz are ideally suited for the next generation of electron energyanalyzer based on time-of-ight techniques

• The greatly reduced operating costs.


Figure 3.4: The universal curve for surface sensitivity in photoemission.Electron inelastic mean free paths from a variety of materials are plottedversus their kinetic energy in the solid (the lowest kinetic energies shownwill not be able to overcome the work function and therefore will not escapethe solid). Indicated on the plot are the kinetic energy ranges for standardARPES and laser ARPES. Figure adapted from [50].

• The very low inelastic background. The reduced photoemission phasespace drastically reduces the number of inelastic photoelectrons, pro-viding spectra with a very small background. This reduction in in-elastic background at low energy is especially helpful in the high Tcsuperconductors. Not only do these materials show an exceptionallylarge inelastic background, but the majority of the electrons near theFermi surface live near the zone edges, beyond the reach of 6 eV ARPES(Fig. 3.5).

• The easy to control of the light polarization vector (linear or circular),which is important to satisfy the stringent APRES matrix elementselection rules and/or for magnetic studies.

There are however some serious issues that can't be neglected as for in-stance:

• The very limited photon energy tunability limits the momentum spaceto very small range of kz, and basically limits the applications to two


Figure 3.5: The furthest momentum space range toward the M point wecan reasonably measure for 6 and 7eV ARPES is shown in green on a Fermisurface of overdoped Pb-Bi2Sr2CaCu2O8+δ measured in the superconductingphase (with synchrotron radiation). The white solid lines correspond to thetight binding t. Note the nite discontinuous Fermi surface with Fermiarcs and gapped regions around the anti-node. The two green light aretwo simulated cut corresponding to a electron analyzer with 30 angularacceptance (the Scienta R4000 for instance). The exact Euler angle of thesample at 6 eV are θ = 30 and φ = 60 and at 7eV, θ = 35 and φ = 60 (φis along the analyzer slit)

.

dimensional or quasi two dimensional systems.

• Final states eects, like kz broadening or more simple band structureeect must be carefully considered (even in 2D systems [52]). Indeed,though the well-dened nal state imposes a strict condition on pho-toelectron transition, the photoelectron nal state is no longer like afree electron for low-energy excitation. Therefore, tuning the photonenergy to the nal state can be critically important. [53]

• As a consequence of the momentum conservation, only a limited rangeof in-plane momentum (k||) can be explored (Fig. 3.5).

Despite these limitations, the scientic interest is spreading quickly withalready three Reviews of Scientic Instruments published since last year (Ref.[54, 55, 56]). This enthusiasms seems already justied by superior level of


bulk sensitivity and momentum/energy resolution that are already revealingnew aspects of the data in term of scattering rate, lineshape and kinks.

Scattering rate

The quasiparticles scattering rate can provide a wealth of informations on thelow energy interactions, and is a very important aspect of the data since it isdirectly connected to transport properties. The cuprate case is particularlyinteresting since the node in the gap allows the existence of quasiparticlescrossing the Fermi level even in the superconducting ground state. Further-more, the nodal quasiparticle show a quasi-linear dispersion, and was early oninterpreted in term of massless fermions with a Dirac-cone dispersion[57, 58].However, the exact doping and temperature dependence has been dicult toextract reliably from ARPES data [5, 6]. The sharp peaks extracted fromlaser ARPES seem to nally overcome some of the associated diculties andshow a good agreement with THz conductivity spectroscopy and STM [59].This consistency allows the ARPES data, which is the only momentum re-solve probe, to be use as a stringent test for various proposed scatteringmechanisms in the superconducting state.

Lineshape

EDCs lineshape are often asymmetric, have an unknown background and areusually complex to t with any model. This explains why MDC analysis ispreferred by most experimentalist. However, the low background, reducednal state broadening eects and increased bulk sensitivity provided by laserARPES seem to have overcome most of these diculties. Laser ARPESEDCs may provide now a solid foundation to test theoretical models. This isremarkably illustrated by the accurate t of the normal state asymmetricalEDC lineshape using a formalism based on the Gutzwiller projection[60].

Kinks

The self energy is now re-explored with unprecedented accuracy and newfeatures can be distinguished. In addition to the low energy kinks at ≈40and ≈70 meV and the high energy anomaly at 300-400 meV[10], two kinks at115 and 150 meV have been reported along the nodal direction in optimallydoped Bi2212[61]. These two new high energy features cannot be attributedto electron coupling with single phonon or magnetic resonance mode andpoint to the existence of a new form of electron coupling in the cuprates.


3.2.2 Experimental setup

At the heart of our laser system is a cavity-dumped, Kerr mode-lockedTi:Sapphire oscillator, pumped with 6 watts from a frequency doubled Nd:Vanadatelaser. The oscillator generates ≈ 100 fs, 30 nJ pulses tunable around 840 nm(≈1.5 eV) at a repetition rate of 1 to 52 MHz. In order to produce ultravi-olet photons, we utilize two and three stages of non-linear second harmonicgeneration through type I phase matching in β-Barium Borate (BBO)[62],resulting in the generation of the fourth harmonic at 210 nm (≈6 eV). Thissetup will produce not only photon pulses at 6eV, but at 3 and 1.5 eV aswell.

3.2.3 Pump-probe ARPES

All these pulses can be delayed from each other with sub-picoseconds accu-racy. This opens the possibility to perform pump-probe ARPES experiments.Indeed, after the absorption of a strong laser pulse, the electrons, phononsor magnetic excitations display dierent temporal evolution. Using laser asa pump and probe for ARPES experiments, it becomes possible to com-bine this information with the electronic structure. This new dimension ofARPES could allow us to dierentiate between dierent scattering channelas a function of momentum revealing nally the tight interplay between or-bital, lattice and spin degrees of freedom or the dierent charge dynamics ofquasiparticles in the nodal regions and the BZ face.

For instance, the electron-hole pair created by photon absorption relaxesrapidly (femtosecond time scale) to a metastable state which then relaxesmuch more slowly through phonon emissions on a picosecond time scale. Re-cent time-resolved studies of reectance in cuprates showed dramatic dopingdependencies on the picosecond time scale[63]. This doping dependence issurprising on two aspect. First the the photo-induced change in reectiv-ity reverses sign at optimal doping. Second, the relaxation time abruptlydrops from 20 ps in the underdoped regime to ≈2 ps at optimal doping.Moreover, it is possible to distinguish quasiparticles in the pseudogap statefrom quasiparticle in the superconducting states from the time dependenceof the change in reectivity in underdoped cuprates[64]. Correlating thesetime dependent results with the self energy and gap information as a functionof momentum would be extremely valuable in addressing the nature of thebuilding block of the superconducting ground state.

This type of pump-probe experiment has been shown to be very promis-ing, notably by the group of Prof. M. Wolf who recently demonstrated some


of the powerful aspects of the technique 1, such as the dynamic of the elec-tronic structure during Insulator-Metal transition [65], the dynamics of theSelf-Energy [66] or the dynamic of the electronic relaxation in HTSC [65].

3.2.4 Preliminary data

Figure 3.6: ARPES laser data on OPT Bi2212 (Tc=92K). Fermi surface withthe characteristic anisotropic gap. The raw data along the nodal direction isshown using a false color map. The FWHM of the energy distribution curve(EDC) at kF along the node is estimated from the high binding energy side(low energy side) to reduce the eect of the Fermi function cuto. This isillustrated with a symmetrized EDC shown with a Lorentzian t in green inthe same panel. The symmetrized EDC stack at kF for various momentumalong the Fermi bananas are shown, displaying a nice d-wave like gap .TheMDC peak position and FWHM as a function of energy is shown on the twotight hand side panels.

1The equipment they use is quite dierent though, and include a regenerative amplierand a time-of-ight electron analyzer


In Fig. 3.6, I show some recent data on OPT Bi2Sr2CaCu2O8+δ takenwith our laser ARPES system. This demonstrates the high quality of datathat can be obtained in term of energy resolution, momentum resolution andbackground level. The MDC dispersion shows a sharp kink at ≈ 61 meVand MDC FWHM shows a linear energy dependence at low binding energy,and a sudden increase around the kink energy in agreement with previousreports [5, 6]. In particular we observe very sharp MDC peak at the Fermilevel with a well dened, symmetric, Lorentzian line shape. The EDC at kFshows a very low high energy background and a very sharp peak as well. Toquantify the peak width without the contribution of the Fermi function, Icopied the high binding energy side of the peak on the right side, and tted aLorentzian to it. As noted already it ref. [49] and discussed in further detailsin ref. [60], the lineshape of this symmetrized EDC seems to agree very wellwith just a simple Lorentzian, which is expected by seldom observed.

3.3 Spin-resolved, time-of-ight ARPES

Despite the fact that much exciting information is likely to be gained in thespin resolution of ARPES, and while there has been much eort toward per-forming these experiments, the inherently low eciency of analyzing electronspin polarization has hindered spin-resolved PES. Past experiments were ac-complished with energy resolutions of 2 orders of magnitude poorer than whatspin-integrated ARPES is now capable of, and with no angle/momentumresolution. With technology turning toward utilizing the electron spin inmaterials and with the rapid expansion of interest in the magnetic propertiesof complex materials and thin lms, the need for performing the completeSpin and Angle Resolved Photoemission Spectroscopy experiment at highresolutions has increased. We have proposed a new solution to overcome thelow eciency encountered by traditional technique (hemispherical energyanalyzer and Mini Mott detector) in the form of new type of momentum-energy-spin analyzer. The concept is based on a homemade high-eciencyspin polarimeter based on low energy exchange scattering, coupled with ahome made Time-Of-Flight (TOF) energy analyzer. We hope to achieve bythis mean eciency up to 100'000 higher than today's state of the art, open-ing nally the door for more thorough and higher resolution Spin-ARPESstudies (Fig. 3.7 and Ref. [67]). With our current TOF abilities, the spec-trometer must be used with a pulsed excitation source with long enoughintervals to allow for a reasonable part of the spectrum to be taken withinone time period. Unfortunately, this currently requires the ALS to be in2-bunch mode, which is only available for two weeks each March and Au-

3.3 Spin-resolved, time-of-ight ARPES 27

Figure 3.7: CAD drawing of the our spin resolved time of ight. The systemhas two lens columns (in red tones). One straight column for TOF-ARPES,and one column with a band pass lter that serves the spin detector. Thesystem was fully build and designed from scratch and is now fully assembleand is currently in the advanced test phase. A photograph of the completesystem at BL 12.0.1 of the ALS is shown.

gust. The Pulsed laser source will have the right photon energy to performvery high momentum resolution, the right pulse length to achieve very highenergy resolution and the optimal repetition rate to run the setup at his fullpotential all year around. On one hand, the ALS oers the possibility totune the photon energy, which is sometime critical to satisfy the stringentAPRES matrix element selection rules. On the other hand, the laser allowsfor a full control of the polarization (linear or circular), a key element formagnetic studies. It is easy to see how these two sources will complementeach other to form a very powerful complete system directly probing all thequantum number of the electronic excitation in solids.

3.3.1 High-eciency spin polarimeter

Though I was involve with the design and development of this apparatus,it is mainly the current thesis work of my colleague student Chris Jozwiak,


who is also about to graduate. Part of my contribution was the designs andcharacterization of the thin lms used in the high-eciency spin polarimeter,which is detailed in the following letter to Phys. Rev. B.

Mapping the spin-dependent electron reflectivity of Fe and Co ferromagnetic thin films

J. Graf,1,* C. Jozwiak,2 A. K. Schmid,1 Z. Hussain,3 and A. Lanzara1,2

1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA2Department of Physics, University of California Berkeley, California 94720, USA

3Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USAsReceived 29 April 2004; revised manuscript received 9 February 2005; published 29 April 2005d

Spin polarized low energy electron microscopy is used as a spin-dependent spectroscopic probe to study thespin-dependent specular reflection of a polarized electron beam from two different magnetic thin film systems:Fe/Ws110d and Co/Ws110d. The reflectivity and spin-dependent exchange-scattering asymmetry are studied asa function of electron kinetic energy and film thickness, as well as the time dependence. The largest value ofthe figure of merit for spin polarimetry is observed for a five monolayer thick film of Co/Ws110d at an electronkinetic energy of 2 eV. This value is 2 orders of magnitude higher than previously obtained with state of the artmini-Mott polarimeter. We discuss implications of our results for the development of an electron-spin-polarimeter using the exchange-interaction at low energy.

DOI: 10.1103/PhysRevB.71.144429 PACS numberssd: 75.70.Ak, 75.75.1a, 73.63.Hs, 73.21.Fg

I. INTRODUCTION

State of the art electron spectrometers have reached anenergy and momentum resolution that allows probing subtleand complex many-body effects. However the low efficiencyof spin detection impedes experimental progress toward ourimproved understanding of the spin degree of freedom incomplex and magnetic materials. In terms of spin-detectordevelopment, a quantity of great interest is defined as thefigure of merit sFOMd and is proportional to the inversesquare of the statistical error in an electron counting experi-ment to measure the polarization of an incident beam.1 Con-ventional spin polarimeterssmini-Mott detectorsd have aFOM below 2310−4 sRef. 2d. This low FOM has long beenrecognized as problematic. For well over one decade, variousgroups have worked on the idea to use exchange scatteringof low energy electrons by ferromagnetic surfaces as a prom-ising route toward achieving significantly improved effi-ciency. For example, detailed investigations of the Fes110dsurface have shown that FOM of the order of 8310−3 can beachieved.3,6Along this direction, different surfaces have beeninvestigated to increase the FOM, the lifetime and thereproducibility.4,5 Recently, FOM up to 6310−3 have beenachieved with a robust system, Fes001d-ps131dO,7,8 and aspin resolved electron spectrometer has been built.9 A differ-ent approach suggested even higher FOMsup to 5310−2dusing high quality ultrathin Co or Fe films on Ws110d.10,11

Unfortunately, the microscopic size of this ultrathin film isproblematical in spin polarimetry applications.9 Here, wedemonstrate that a larger film of lower quality that can beeasily grown and reproduced at room temperature can indeedreliably achieve very high FOM.

In this paper, we report a detailed study of the reflectivityand spin-dependent exchange-scattering asymmetry as afunction of electron kinetic energy and film thickness and asa function of time for two different magnetic thin filmsystems grown at room temperature: Fe/Ws110d andCo/Ws110d. The results confirm the possibility of construct-ing novel spin polarimeters with FOM up to 2 orders

of magnitude higher than state of the art mini-Mottpolarimeter and stray fields significantly lower thancurrent exchange-scattering-based polarimeters using bulkferromagnets.

II. EXPERIMENTAL TECHNIQUE

The data reported here are taken with a spin polarized lowenergy electron microscopesSPLEEMd12 located in the Na-tional Center for Electron Microscopy of the Lawrence Ber-keley National Laboratory. SPLEEM is a powerful tool toimage the dynamics of surface magnetic microstructures inthe subsecond time scale, and its sensitivity to the samplesurface allows the imaging of atomic steps with a lateralresolution of,20 nm. Here, we use it as a fast and powerfulspin-dependent electronic probe by recording the number ofelastically backscattered electrons as a function of their spinand energy.

Cobalt and iron films were prepared at room temperatureby electron beam evaporation of high-purity material on as110d tungsten crystal. The tungsten substrate was cleaned bysuccessive flash heating cycles in an O2 environment of10−8 Torr, followed by flash heating in UHV up to<2000°C. The substrate cleanliness was monitored by Au-ger electron spectroscopy and no traces of contaminationwere detected. The base pressure was on the order of10−11 Torr and was in the low 10−10 Torr region during filmdeposition. The deposition rate was measured by direct ob-servation with SPLEEM and adjusted to approximately 0.1monolayersML d per minute. Both Co and Fe grow in a quasilayer-by-layer mode at room temperature, as previouslyreported.13,14 More specifically, Fe grows in a pseudomor-phic mode for the first 1.8 ML, and then relaxes to a bulk bccstructure. The cobalt film adopts a pseudomorphic structurefor the first ML and then transforms to a close-packedstructure.15

Figures 1sad and 1sbd show images of the magnetic sur-face for Co/Ws100d s1ad and Fe/Ws110d s1bd at a certainenergy and film thickness. The bright areas represent flat

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terraces on the crystal surface and the darker curving linesand bands represent the monoatomic steps and multilayerstep bands of the Ws110d surface. A blue and a red regioncan be observed for both images. These two regions repre-sent two magnetic domains with opposite magnetizationsblack arrowsd. The white arrows represent the majority spinorientation of the illumination electron beam. Within the im-aged field of view, regions of interestsROId where substratestep density is low and film magnetization is homogeneouslyaligned in a particular magnetic domainfsee the black con-tour in Figs. 1sad and 1sbdg are selected. The average inten-sity at a given electron energy, film thickness and spin ori-entation is extracted in these regions. The spin polarizationof the illuminating electron beam was adjusted to be alignedwith the magnetic easy axis of the film. Continuous se-quences of images of the surfaces were then recorded auto-matically, during the simultaneous deposition of the ferro-magnetic thin films. For each set of two consecutive images,the spin orientation of the electron beam was toggled to beparallel and antiparallel to the film magnetization. The depo-sition rate was adjusted to be sufficiently slow so that duringthe deposition of each ML we were able to ramp severaltimes the electron beam energy from 0 to 13 eV in steps of0.2 eV swith respect to the vacuum leveld. The average in-tensity in the selected ROI is then measured for each imageand normalized with respect to the electron illumination in-tensity.

III. RESULTS

Figures 1scd and 1sdd shows a color plot representing theaverage reflectivity for cobaltsirond vs the electron energyshorizontal axisd and the film thicknesssvertical axisd. Thevariations in the reflectivity seem to have at least two peri-odic components. The component that is visibly energy in-dependentfsee the white arrows in Fig. 1sddg is due to thevarying density of steps during deposition. The reflectivityminima sin blackd coincide with half completed monolayersshigher surface step densityd and the maximasin redd occurwith the completion of each monolayerslow surface stepdensityd. These growth oscillations are most clear at smallfilm thickness and are used to calibrate the film depositionrate. The interesting component is energy dependentand looks like hyperbolic shaped maximasin redd andminima sin blackd in the reflectivity plotssmore pronouncedfor Co/Ws100dd. This is a bulk and intrinsic effect knownas the “quantum size effect”sQSEd.10,16 More specifically,a ferromagnetic slab acts like a resonant cavity and inducesinterference patterns. The QSE is more pronounced forCo/Ws110d sFig. 1scdd than for Fe/Ws110d sFig. 1sdddfilms. We attribute this attenuation to previously reportedkinetic roughening during room temperature growth ofFe/Ws110d.10

In Figs. 1sed and 1sfd, we report the spin asymmetry ver-sus energy and film thickness for Co/Ws110d and Fe/Ws110dfilms, respectively. Here, the spin asymmetrysor Shermanfunctiond is defined by

As =1

P

R↑↓ − R↑↑R↑↓ + R↑↑

,

whereP is the polarization of the electron beams20%d andR↑↑ sR↑↓d is the reflectivity for electrons with spin parallelsantiparalleld to the magnetization of the film. The whitedashed lines at 2 ML film thickness in Figs. 1sed and 1sfdclearly separate a uniform black region from a modulated redand blue region. The featureless black region indicates a per-fect symmetry in both Fe and Co films reflectivity. This canbe explained by noting that the Curie temperaturesTcd ofFe/Ws110d films is above room temperature only for filmthicknesses greater than 2 ML.17 We attribute the absence ofspin asymmetry in thin Co films to a similar depression ofthe Curie temperature. The remarkably perfect symmetry ofthe measurement above Tc supports the magnetic origin ofthe asymmetry measured below Tc.

Figure 2sad shows energy scans of the spin-dependent re-flectivity for different Co film thicknesses. For each filmthickness, two main observations can be made about the spindependent reflectivity:

s1d The reflectivity for the anti-parallel spinsred curvedshows a red shift with respect to the case of parallel spinsblue curved.

s2d The reflectivity oscillation in the case of spin parallelsblue curved are damped with respect to the antiparallel spincasesred curved.These observations suggest that two mechanisms contributeto the total spin asymmetry. The spectra for film thicknessbigger than 5–6 ML are mainly dominated by the damping

FIG. 1. sColor onlined Panelssad andsbd show SPLEEM imagesof Co/Ws110d and Fe/Ws110d films, respectively. For both films themagnetic easy axis points along the horizontal direction in the im-ages. Both images were recorded with electron spin polarizationaligned to the rightswhite arrowd. The magnetic domains are shownwith blue and red contrast; the magnetization direction of the do-mains is indicated by black arrows. Black contours are the regionsof interest for average reflectivity measurements.scd,sdd Color-scaleplots of the measured reflectivity as a function of the electron ki-netic energyshorizontal axisd and film thicknesssvertical axisd forboth thin-film systems.sed,sfd Color-scale plots of the spin asym-metry of the reflectivity.

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mechanism. We attribute the damping to different mean freepaths for spin parallel or antiparallel to the majority spin.Indeed it is known that the so-called universal curve predictstoo large a value of the inelastic mean free pathsIMFPd fortransition metals at low energy, and spin-dependent values ofthe IMFP corresponding to a few monolayers have been re-ported at the energies considered in this paper.18–20 Theseresults suggests that SPLEEM can be used as a tool to extractinformation on the spin-dependent mean free path, a funda-mental quantity for many properties of solids. A more de-tailed study is required.

The red shift of the antiparallel spin reflectivity spectracan be clearly observed in Fig. 2sbd, where the spin-dependent reflectivity for a 4 ML thick Co/Ws110d film isshown. We see that the large gradients of the reflectivityinduced by the quantum well states are slightly shifted forelectrons of opposite spin due to the exchange splitting of theband structure. The minima and the maxima of the reflectiv-ity indicated with the blue and red arrows are shifted by 0.3and 0.15 eV, respectively. It is the combination of this energyshift with the large gradients in the reflectivity that causes asignificant enhancement or reduction of the magnetic asym-

FIG. 3. sColor onlined sad,sbd Color-scaleplots of the “figure of merit” for Co/Ws110d andFe/Ws110d thin films, respectively, as a functionof the electron kinetic energyshorizontal axisdand film thicknesssvertical axisd. scd,sdd The re-spective figure of merit, plotted as a function ofenergy for Co and Fe at different thicknesses. Forclarity, the energy scans are incrementally shiftedby 10−2. The location of the scans is shown bycolor horizontal lines in panelssad and sbd.

FIG. 2. sColor onlined sad Energy dependenceof the reflectivity for spin parallel and antiparallelto the Co/Ws110d film magnetic axis for differentfilm thickness. The energy scans are incremen-tally shifted by 0.05.sbd Expanded view of thespin dependence of the reflectivity for the 4 MLthick film. scd Spin asymmetry for a 4 ML thickCo/Ws110d film obtained from Fig 1sbd. sdd Bandstructure calculation for a 4 ML thick Co/Ws110dfilm sRef. 16d.

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metry, as shown in Fig. 2scd. This seems to be the dominantmechanism at small film thickness even in the presence ofsome inelastic damping.

Figure 2sdd shows a band structure calculation alongthe perpendicular direction for a 4 ML Co/Ws110d thinfilm.16 From the band structure calculation and the measuredspin asymmetry, one can see that the first maxima at2.6 eV of the spin asymmetry may have a contributionfrom the exchange-split band gap. But there is no bandgap at the second maxima at 4.7 eV and one can see againthe strong contribution of the finite size at small filmthicknesses.

In Figs. 3sad and 3sbd, the dependence of the figureof merit sFOMd on electron kinetic energyshorizontal axisdand film thickness svertical axisd for Co/Ws110d andFe/Ws110d is shown. The figure of merit combines thereflectivity and the spin asymmetry and is defined byAs

2(sR↑↓+R↑↑d /2). This whole map of the figure of merit em-phasizes the important role of the QSE oscillations for spindetection. The FOM is in fact very sensitive to the film thick-ness and electron energy. A maximum for the FOM isreached only in a narrow range of energy and film thickness.This feature must be taken into account for the furtherdevelopment of electron spin polarimetry. In Figs. 3scd and3sdd, several cuts in energy of the figure of merit forCo/Ws110d and Fe/Ws110d are shown, respectively. TheFOM of Co/Ws110d displays a pronounced maximum of 0.02for 5 ML film thickness at an electron kinetic energy of 2 eV.In Fe/Ws110d we have found a maximal FOM of 0.01 at 3.2eV for 4 ML film thickness. These results clearly show thatthe Co/Ws110d thin film gives a higher value of FOM thanthe Fe/Ws110d thin film when the films are grown at roomtemperature.

We also address a known difficulty in exchange-scatteringpolarimetry related to surface conditions of the magneticfilms used. Over the course of many hours or days, the ad-sorption of contamination from rest gas present in UHV con-siderably reduces both the reflectivity and the spin asymme-try of the film saging effectsd. In a spin-detector applicationsuch aging effects cause degradation of the FOM over timeand therefore cause considerable losses of efficiency. To fullycharacterize the Co/Ws110d 5 ML thin film sthe one leadingto the highest FOMd, we have performed a detailed time andannealing temperature dependence of the reflectivity. For thispurpose, freshly grown films were stored in an annex cham-ber with a base pressure of 2310−9 Torr to study the effectsof UHV contamination.

Figures 4sad and 4sbd shows how the high reflectivityand asymmetry of a 5 ML thick Co film, measured every 24h for 3 days, evolve with time. One can see that already after24 h the reflectivity is substantially suppressed, the spinasymmetry is reduced by 50%, and the maximum FOM isdiminished by almost 90%. We found that this aging effectcan be easily reversed with a thermal treatment. Figures 4scdand 4sdd show how careful annealing leads to substantialrecovery of the film’s original exchange-scattering character-istics s75% of the original FOMd. Additional heatingsTù330°Cd causes the disruption of the film with theformation of three-dimensional islands surrounded by athin pseudomorphic filmsStranski-Krastanov film morphol-

ogyd. On the other hand, the effect of UHV contamination oniron is even more severe, and the FOM could not besignificantly recovered by annealing before film disruption.Neither film’s FOM could be recovered after exposure to theatmosphere.

A complete characterization would require the incidentangular acceptance of both systems, but it cannot be mea-sured by low energy electron microscopy where only thebackscattering of normal incident electrons is measured.Nevertheless the angular spread of electron is by definitionvery small in angle resolved photoemission spectroscopy,particularly with high efficiency electron spectrometers liketime of flight spectrometers.21

IV. SUMMARY AND CONCLUSIONS

In conclusion, we presented a comparative analysis ofthe figure of merit as a function of thickness, energy andtime of two promising thin film systems using an innovative

FIG. 4. sColor onlined Aging effects and regeneration for a 5ML thick cobalt film: sad Evolution of the reflectivity of the filmwith time in UHV conditions. Redsblued energy scans representincident electrons with spin polarization parallelsantiparalleld to themagnetization. For clarity, each curve is shifted by 0.01.sbd Thespin asymmetry calculated from the reflectivity distribution curvesin panel sad. The effect of annealing on the reflectivity and thecorresponding spin asymmetry are shown inscd and sdd, respec-tively, after 56 h of room-temperature aging in UHV.

GRAF et al. PHYSICAL REVIEW B 71, 144429s2005d

144429-4

technique based on spin polarized low energy electron mi-croscopy. We have shown that Co/Ws110d thin film is anideal system for exchange-scattering based electron spin po-larimetry, giving a figure of merit as high as 0.02 with verylow stray fields and thus without spurious asymmetry. Inaddition, because of the homogeneity of Co/Ws110d thinfilms grown at room temperature and the possibility of re-versing aging effects by moderate annealing, this system ap-pears particularly stable for spin polarimetry applications.

ACKNOWLEDGMENTS

We thank G.-H. Gweon, M. Portalupi, and Z. Q. Qiu forhelpful discussions. This work was supported by theDirector,Office of Science, Office of Basic Energy Sciences, Divisionof Materials Sciences and Engineering, of the U.S. Depart-ment of Energy under Contract No. DE-AC03-76SF00098.We acknowledge the support of the National Science Foun-dation through Grant No. DMR-0349361, the A. P. SloanFoundation, and the Hellman Foundation.

*Electronic address: [email protected]. Kessler,Polarized ElectronssSpringer-Verlag, Berlin, New

York, 1985d.2D. T. Pierce, R. J. Celotta, M. H. Kelley, and J. Unguris, Nucl.

Instrum. Methods Phys. Res. A266, 550 s1988d.3G. Fashold, M. S. Hammond, and J. Kirschner, Solid State

Commun. 84, 541 s1992d.4F. U. Hillebrecht, R. M. Jungblut, L. Wiebusch, C. Roth, H. B.

Rose, D. Knabben, C. Bethke, N. B. Weber, S. Manderla, U.Rosowskiet al., Rev. Sci. Instrum.73, 1229s2002d.

5R. Jungblut, C. Roth, F. U. Hillebrecht, and E. Kisker, Surf. Sci.269–270, 615 s1992d.

6M. S. Hammond, G. Fahsold, and J. Kirschner, Phys. Rev. B45,6131 s1992d.

7R. Bertacco and F. Ciccacci, Surf. Sci.419, 265 s1999d.8R. Bertacco, M. Merano, and F. Ciccacci, Appl. Phys. Lett.72,

2050 s1998d.9R. Bertacco, M. Marcon, G. Trezzi, L. Duo, and F. Ciccacci, Rev.

Sci. Instrum.73, 3867s2002d.10R. Zdyb and E. Bauer, Surf. Rev. Lett.9, 1485s2002d.

11R. Zdyb and E. Bauer, Phys. Rev. Lett.88, 166403s2002d.12E. Bauer, T. Duden, and R. Zdyb, J. Phys. D35, 2327s2002d.13U. Gradmann and G. Waller, Surf. Sci.116, 539 s1982d.14T. M. Gardiner, Thin Solid Films105, 213 s1983d.15E. Bauer, J. Phys.: Condens. Matter11, 9365s1999d.16T. Scheunemann, R. Feder, J. Henk, E. Bauer, T. Duden, H. Pink-

vos, H. Poppa, and K. Wurm, Solid State Commun.104, 787s1997d.

17H. J. Elmers, J. Hauschild, H. Fritzsche, G. Liu, U. Gradmann,and U. Kohler, Phys. Rev. Lett.75, 2031s1995d.

18D. P. Pappas, K.-P. Kamper, B. P. Miller, H. Hopster, D. E.Fowler, C. R. Brundle, A. C. Luntz, and Z.-X. Shen, Phys. Rev.Lett. 66, 504 s1991d.

19F. Passek, M. Donath, and K. Ertl, J. Magn. Magn. Mater.159,103 s1996d.

20M. Getzlaff, J. Bansmann, and G. Schönhense, Solid StateCommun. 87, 467 s1993d.

21O. Hemmers, S. B. Whitfield, P. Glans, H. Wang, D. W. Lindle,R. Wehlitz, and I. A. Sellin, Rev. Sci. Instrum.69, 3809s1998d.

MAPPING THE SPIN-DEPENDENT ELECTRON… PHYSICAL REVIEW B 71, 144429s2005d

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3.4 Inelastic x-ray scattering from collective atom

dynamics

The study of atomic dynamic using inelastic neutron scattering is a very pow-erful technique. The neutron energy loss spectrum as a function of diractionangle is directly related to the dynamic structure factor S(Q, E), which isthe time and space Fourier transform of the density correlation function [68].Neutrons are particularly suitable for the following reasons:

• The neutron-nucleus scattering cross-section is suciently weak to al-low for a large penetration depth

• The momentum of the neutron may be used to probe the dispersionout to several Å−1

This is in contrast with inelastic light scattering techniques like Brillouinor Raman scattering, which can only probe acoustic and optic modes closeto the BZ center.

While there are no theoretical reason not to use X-rays, the energy reso-lution posed a great experimental challenge and hindered the development ofinelastic x-ray scattering (IXS). Considering that photons with a wavelengthof λ = 0.1nm have an energy of about 12keV, the study of phonon excitationsin solids require a resolutions in the meV range. That is a relative resolutionof ∆E/E ≈ 10−7. However, IXS oers some clear advantages. X-ray canbe focused down to a few tens of micrometers, allowing to probe sample assmall as a few 10−6mm3. This is the key breakthrough that allowed us tostudy cuprates like Bi2Sr2−xCu2O6+δ. In addition, it oers the possibility todo it under extreme thermodynamic conditions, such as very high pressure.To date, there are only four instruments in the world. two at the EuropeanSynchrotron Radiation Facility (ESRF), one at the Advanced Photon Sourceat Argonne National Laboratory and one at SPring-8 in Japan. The datapresented in this thesis were collected at the beamline ID28 at ESRF andBL35XU in SPring-8. Most of the facts and informations describe in thisshort introduction can be found on the beamlines websites (ref. [69, 70]) andin ref. [71]. More details on the apparatus can be found in ref. [72, 73, 74].

3.4.1 Scattering kinematics

The inelastic scattering process is depicted schematically in Figure 3.8.The momentum and energy conservation impose that:

Q = ki − kf

3.4 Inelastic x-ray scattering from collective atom dynamics 35

Figure 3.8: Schematics of the inelastic scattering process. The incident andscattered photons are characterized by their energy E, wave vector k andpolarization vector ε

E = Ei − EfQ2 = k2

i + k2f − 2kikfcos(θ)

where θ is the scattering angle between the incident and scattered pho-tons. The dispersion relation for photons is given by: E(k) = ~ck. Con-sidering that the energy losses or gains associated to phonon-like excitationsare always much smaller than the energy of the incident photon (E Ei),one obtains:

Q/ki = 2sin(θ/2)

The ratio between the exchanged momentum and the incident photonmomentum is completely determined by the scattering angle. Therefore, forIXS, there are no limitation in the energy transfer at a given momentumtransfer for phonon-like excitations, in strong contrast to INS where a strongcoupling between energy- and momentum transfer exists.

The experimental setup consists of a high energy resolution backscatter-ing monochromator, consisting of a silicon crystal oriented along the (111)direction. The photons from the pre-monochromator are backscattered atthe Bragg angle of 89.98and focused on the sample using a toroidal mirror.The X-rays scattered by the sample are energy analyzed using another siliconcrystal operating at the same reection order as the monochromator and asilicon diode.

In the case of ID28, there are in fact ve independent analyzer systemswith a xed angular oset between them. There mounted on a 7-meter armthat rotate in the horizontal plane allowing to choose the scattering angle.


In the case of BL35XU, 12 independent analyzer systems are mounted in a4x3 (HxV) array on a 10 meters analyzer arm (see g. 3.9).

Figure 3.9: IXS detector arm at SPring-8

In this backscattering geometry, the energy dierence between the ana-lyzer and the monochromator reection is not set by adjusting one of the twoBragg angles, but by changing the relative temperature of the two crystaland consequently the lattice parameters and the reected energy. Practically,the temperature of the analyzer is set constant while one scan the temper-ature of the monochromator. For silicon at room temperature, a relativeenergy resolution ∆E/E of ≈ 10−9 require to control the temperature of themonochromator crystal with a precision of about 0.5mK while keeping theanalyzer temperature constant within a mK over hours.

The relative energy resolution depends on the Bragg reection used aswell. Indeed it can be shown that the energy resolution is proportional tothe lattice spacing associated with the reection order [71]. In this thesis,only the 8 8 8 and 9 9 9 reections were used, since they provided thebest compromised between photons ux and energy resolution. The keyparameters are listed in table 3.1

3.4 Inelastic x-ray scattering from collective atom dynamics 37

Reection Energy Flux ∆E(keV) (photons/sec) (meV)

Si(7,7,7) 13.840 10.5 ×1010 7.6±.2Si(8,8,8) 15.816 9.0 ×1010 5.5±.2Si(9,9,9) 17.794 2.7 ×1010 3.0±.2

Si(11,11,11) 21.747 6.6 ×109 1.5 ±.1

Table 3.1: IXS beamlines specications

3.4.2 Dierential cross-section

If we limit ourselves to consider the case in which the electronic part of thetotal wave function is not changed by the scattering process 2 and we assumethe validity of the adiabatic approximation3, the double dierential cross-section is proportional to the number of incident probe particles scatteredwithin an energy range δE and momentum variation Q into a solid angle δΩ.

∂2σ

∂Ω∂E= r2

0(εiεf )2 kikf|f(Q)|2 S(Q, E)

where f(Q) is the atomic form factor, r0 is the classical electron radius.For this specic case, the coupling characteristics of the photons to the sys-tem, the Thomson scattering cross section, is separated from the dynamicalproperties of the system, and the atomic form factor f(Q) appears only asa multiplicative factor. We considered here the case for a system composedof a single atomic species. For a molecular or crystalline systems one mustsubstitute the atomic form factor with either the molecular form factor, orthe elementary cell form factor, respectively. Note that the total absorp-tion cross-section of X-rays is usually limited by the photoelectric absorptionprocess (proportional to Z4), and not by the Thomson scattering process(proportional to Z2). Therefor, the Thomson scattering channel is not veryecient for system with high Z in spite of the Z2 dependence. This canbe very problematic for bismuth family of the cuprates. This limitation canhowever be overcome to a certain extent by working in higher BZ, where theQ2-increases of the inelastic cross section can partly compensate.

2This basically means that we assume the dierence between the initial state and thenal state is due only to excitations associated to atomic density uctuations.

3This approximation is particularly good for exchanged energies that are small withrespect to the excitations energies of electrons in bound core states: this is indeed the casein basically any atomic species when considering phonon energies.


Chapter 4

The isotope eect

Shortly after the discovery of the isotope eect on Tc in conventional super-conductors [75], it was proposed that quanta of lattice vibration (phonons)are the glue of the superconducting electron pairs (BCS model) [34]. How-ever, due to the small isotope eect in the cuprates and a Tc well beyondthe BCS model, the role of phonons was neglected in HTSC. This was untilARPES unraveled that despite the appearance, the lattice may still play akey role in HTSC [38].

Indeed, by selecting a specic momentum range, we can rst isolate withARPES a specic type of quasiparticle at the Fermi Level. We can thenprogressively increase the excitation energy and study how the quasiparti-cles go through successive shake-o or undressing and turns into simplerexcitations. The well-known ARPES kink at 40-70 meV [36, 37, 38, 76, 77]is one of the best examples of quasiparticles undressing. In this case, thelow energy excitations are dressed into well dened coherent excitations bya collective mode like phonons, plasmon or magnons.

To disentangle the role of the lattice from other bosonic excitations like forsay magnetic modes, we proposed to combine the isotope substitution withARPES. Indeed, the substitution of the oxygen isotope 16 with the isotope18 will soften some of the phonons modes energy. If the lattice plays anyrole, subsequent change in the electron self energy should be observed withARPES. From a rst order approximation (Migdal-Eliashberg), we expect ared shift of the mode energy upon the substitution of the O16 isotope withthe O18 isotope and no other eects away from the mode energy.

We collected ARPES data on optimally doped Bi2Sr2CaCu2O8+δ withTc=91K. The detailed analysis of the isotope eect as a function of crystalmomentum and binding energy turned out to be very successful [7]. The ex-periment demonstrated the underestimated subtle roles of phonons (beyondMigdal-Eliashberg) and their strong correlation with the superconducting

40 The isotope eect

order parameter. This ndings lead to another very interesting result: theanomalously high binding energy ( 70meV) at which the isotope eect isthe strongest. Though we proposed that this eect on the broad incoher-ent hump could be due to higher order scattering eects (multiple phonons)[78, 79, 80], it was clear that we needed a better understanding of this broadincoherent hump. We proceeded in two steps. First, we needed to betterunderstand the origin of this phonon mode. Second, we need to investigatein detail the spectral function at high binding energy. The results of thisstudy unveiled a rich and complex behavior that is described in chapter 6.

In order to address the rst question: the origin of the phonon mode, andit's eect on the band structure we undertook IXS measurement to probe forthe time the exact phonon spectrum in the Bismuth compounds. The resultsof this study are discussed in the next section.

The original letter is reproduced here.

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Supplementary Information accompanies the paper on www.nature.com/nature.

Acknowledgements This work is based on observations made at the European Southern

Observatory, Paranal, Chile, and with the NASA/ESA Hubble Space Telescope obtained at the

Space Telescope Science Institute, which is operated by the Association of Universities for

Research in Astronomy (AURA). We thank R. Somerville for information on the GOODS/CDFS

mock catalogue. We are grateful to the GOODS Team for obtaining and releasing the HST and

FORS2 data

Competing interests statement The authors declare that they have no competing financial

interests.

Correspondence and requests for materials should be addressed to A.C. ([email protected]).

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An unusual isotope effect ina high-transition-temperaturesuperconductorG.-H. Gweon1, T. Sasagawa2,3, S.Y. Zhou4, J. Graf1, H. Takagi2,3,5,D.-H. Lee1,4 & A. Lanzara1,4

1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley,California 94720, USA2Department of AdvancedMaterials Science, University of Tokyo, Kashiwa, Chiba277-8561, Japan3CREST, Japan Science and Technology Agency, Saitama 332-0012, Japan4Department of Physics, University of California, Berkeley, California 94720, USA5RIKEN (The Institute of Physical and Chemical Research), Wako 351-0198,Japan.............................................................................................................................................................................

In conventional superconductors, the electron pairing that allowssuperconductivity is caused by exchange of virtual phonons,which are quanta of lattice vibration. For high-transition-temperature (high-Tc) superconductors, it is far from clear thatphonons are involved in the pairing at all. For example, thenegligible change in Tc of optimally doped Bi2Sr2CaCu2O81d

(Bi2212; ref. 1) upon oxygen isotope substitution (16O !18O

leads to Tc decreasing from 92 to 91K) has often been taken tomean that phonons play an insignificant role in this material.Here we provide a detailed comparison of the electron dynamicsof Bi2212 samples containing different oxygen isotopes, usingangle-resolved photoemission spectroscopy. Our data show defi-nite and strong isotope effects. Surprisingly, the effects mainlyappear in broad high-energy humps, commonly referred to as‘incoherent peaks’. As a function of temperature and electronmomentum, themagnitude of the isotope effect closely correlateswith the superconducting gap—that is, the pair binding energy.We suggest that these results can be explained in a dynamic spin-Peierls picture2, where the singlet pairing of electrons and theelectron–lattice coupling mutually enhance each other.We compare angle-resolved photoemission spectroscopy

(ARPES) data of optimally doped Bi2212 samples at the threedifferent stages of the isotope substitution loop 16O !18O !16O(SupplementaryMethods). In this way, we study directly the impacton the electron spectral function due to a modification of phononproperties, and thus gain insights into the nature of electron–phonon interaction in this material. Here we use the term ‘phonons’loosely to denote quanta of lattice vibrations including spatiallylocalized ones3,4. To ensure that material properties unrelated to theisotope mass did not change during the isotope substitutionprocess, we controlled the sample growth condition with highprecision (Supplementary Methods) and checked the sample qual-ity with various post-growth characterization tools, includingARPES itself (Supplementary Figure). All ARPES data wererecorded at the Advanced Light Source as detailed elsewhere5.Figure 1 shows low temperature (25K) ARPES spectra and their

dispersions along the nodal (GY) direction, where the supercon-ducting gap is zero. In this and the rest of the figures, blue, red andgreen represent results for 16O, 18O and re-substituted 16OR

(18O !16O) samples, respectively. In Fig. 1a, raw ARPES spectraas a function of energy (that is, the energy distribution curves,EDCs) are shown for different momenta along the nodal direction.Each EDC shows a peak, which sharpens up as momentum (k)approaches the normal state Fermi surface6. We loosely refer to asharp peak as a ‘coherent peak’ (CP), and a broad hump as an‘incoherent peak’ (IP)7. We have no intention of implying that theenergy and the width of CPs satisfy the Landau quasiparticlerequirement.Making a comparison between the blue and red curvesin Fig. 1a, we detect definite but small isotope effect. The mostnotable change is the shift of the peak position in curves 4 and 5 byapproximately 15meV, which is bigger than our error bar by a factorof three. Inspecting curves 1–6 in Fig. 1a, we note that the isotopeeffect is maximum for binding energy in the range of 100–300meV,and vanishes as energy decreases (cut 1) and increases (cut 6) fromthis region. We note that this energy range coincides with range of Jto 2J, where J is the super-exchange interaction of neighbouringspins.Figure 1b shows the dispersions derived from the ARPES spectra

at fixed energies as a function of momentum, known as themomentum distribution curves (MDCs). As reported earlier6,8–12,we observe a ‘kink’, that is, a change of the slope in the dispersion, atenergy ,70meV. This feature has been used as evidence that abosonic mode renormalizes the electron dynamics13. A comparisonbetween the 16O and 18O dispersions in Fig. 1b clearly shows that thekink separates the low-energy regime where the spectra show CPand negligible isotope effect, from the high-energy regime where thespectra show IP and appreciable isotope effect. This observationsuggests that phonons contribute appreciably to the electron selfenergy. To illustrate the size of our error bar, we show the dispersionof the 18O !16O re-substituted sample as the green line in Fig. 1b.Clearly the experimental uncertainties caused by isotope substi-tution are smaller than the isotope-induced changes reported here.We note that the insensitivity to isotope substitution at low energiesis consistent with the notion of ‘universal nodal quasiparticle

letters to nature

NATURE |VOL 430 | 8 JULY 2004 | www.nature.com/nature 187© 2004 Nature Publishing Group

properties’ inferred from the doping independence of nodal Fermivelocity11. The marked increase of the EDC width above the kinkenergy (Fig. 1a and ref. 6) and the concurrent strengthening of theisotope effect suggest that this broadening is at least partly due toscattering of electrons by phonons. Figure 1b inset shows the realpart of the electron self energy (S) as a function of energy (q),ReS(q), obtained frommeasuring the deviation of the experimentaldispersion from a common straight line representing the bandstructure dispersion14. We regard ReS(q) mainly as a tool tozoom in on the isotope-induced changes in the dispersion. Asexpected, the overall isotope-induced change in ReS(q) extends upto very high energy. Additionally, themaximum position of ReS(q),that is, the kink energy14, shows an isotope-induced redshift.Both our EDC and MDC analyses show that phonons have

important effect on the electron dynamics in the energy range100–300meV. We note that in the same energy range it is believedthat magnetic fluctuations also contribute importantly to theelectron self energy15. We also note that the fact that the isotopeeffect of ReS(q) extends up to very high energy goes well beyond theMigdal–Eliashberg model, where the phonon effect is confined nearthe kink energy16.In Fig. 2a, we report the evolution of the isotope effect as the

electron momentum approaches the antinodal region near the Mpoint, where the d-wave superconducting gap reaches its maximum(see Fermi surface diagram in Fig. 2d inset). For cuts 2–6, where a

non-zero superconducting gap exists, the MDC dispersion is shownonly up to the gap edge.We defer the discussion of the isotope effecton the gap to later in this Letter. At low energy, a kink in thedispersion can be clearly identified for all cuts (see arrows),becoming stronger for near-antinodal cuts5,12,17. For all cuts, thekinks show an isotope induced redshift, (5–10) ^ 5meV. As inFig. 1, the kink energy defines a crossover from the low-energyregime where the spectra show CP and negligible isotope effect, tothe high-energy regime where the spectra show IP and strongisotope effect. Again, this result suggests that phonons are indeedkey players in causing the kink5,6,17. At higher energy, the isotope-induced changes increase significantly as the momentum gets closerto the antinodal region. Moreover, a subtle sign change of theisotope effect is observed near cut 3. The results in Fig. 2a areconfirmed by raw MDC data—for example, those shown in Fig. 2b.As noted earlier, isotope-induced changes are fully reversible uponisotope re-substitution (green line).

In Fig. 2c we show the raw EDC spectra at the momentum value

Figure 2 Isotope-induced changes of the off-nodal dispersions in the superconducting

state. The ARPES data were taken on optimally doped Bi2Sr2CaCu2O8þd samples with

different oxygen isotopes at T ¼ 25 K. In this figure, k denotes the momentum value

parallel to the M–Y axis (inset in d). a, MDC dispersions for various cuts parallel to G–Y

(see inset in d). A different origin of the momentum axis is used for each cut for an easy

view of all data. Inset shows the isotope shift, measured at the momentum value for which

the isotope-averaged binding energy is 220 meV, versus the superconducting gap (D),

isotope-averaged. The strong linear correlation (dashed line is a guide to the eye) is

independent of the binding energy used. b, Raw MDCs at binding energy (BE) ¼ 200 meV

for the data of cut 6, confirming the fit results of a. c, Raw EDCs at k ¼ 0 (see inset in d)

for cut 6. A large reversible isotope-induced shift (about 230 meV) of the EDC peak

position is observed at high energy. Additionally, a small CP due to the well-known

superstructure (SS) replica is observed (also, see Supplementary Figure). The large MDC

and EDC shifts are fully reversible upon the isotope re-substitution process (green in

panels b and c). d, EDC dispersions for cut 7 (inset), extracted from the maximum

intensity positions of EDCs. The data show a large isotope-induced shift at high energy,

similarly to the data in a. Note also that the EDC dispersion shows a qualitatively different

behaviour from the MDC dispersion, for example, those shown in a, namely completely

separate low-energy and high-energy branches. This difference stems from the fact that

near the kink EDC line shape shows a two-peak structure (for example, Fig. 2 of ref. 6)

while MDC line shape continues to show a single peak.

Figure 1 Isotope-induced changes of the nodal dispersion. The ARPES data were taken

on optimally doped Bi2Sr2CaCu2O8þd samples with different oxygen isotopes at

T ¼ 25 K, that is, in the superconducting state, along the nodal (G–Y) direction. a, Isotope

dependence of raw EDCs. Inset shows a quadrant of the Brillouin zone, divided by the

Fermi surface (curve) into electron-filled (shaded) and electron-empty parts. The

momentum values corresponding to EDCs are marked in the inset and in b (dashed lines).

The spectra show a coherent peak (CP) at low energy, almost isotope-independent, and a

broad hump, that is, an incoherent peak (IP), strongly isotope dependent. The two mix in

the crossover region (curve 3). Throughout this Letter, we use ‘energy’ and ‘binding

energy’ interchangeably. All curves were scaled to the same peak height, and vertically

displaced by different amounts for easy viewing. A small peak at the Fermi energy (0) in

curve 6 is the well-known superstructure (SS) replica of the main band (also, see

Supplementary Figure). b, Isotope dependence of MDC dispersion, obtained by lorentzian

fit of MDCs. The symbol k denotes the momentum value parallel to the G–Y direction.

Consistent with a, the low energy dispersion is nearly isotope-independent, while the

high energy dispersion is isotope-dependent. The effect is fully reversed by isotope

re-substitution (green). The fits are shown only up to 300 meV, because they become less

accurate at high energies. Inset shows the real part of the electron self energy, ReS(q),

obtained from the MDC dispersion14 by subtracting a line approximation for one electron

band e (k), connecting two points, one at E F and the other at 300 meV binding energy, of

the 18O dispersion. The kink position, defined as the binding energy of the peak in ReS(q),

undergoes a redshift upon isotope substitution (see arrows).

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marked with a grey-filled circle in Fig. 2d inset. Here a shift of about230meVof the IP is observed. This value is a factor of 2 larger thanthemaximum shift reported along the nodal direction (see cut 1 andFig. 1a). The weak low energy CP in each EDC of Fig. 2c is the well-known weak superstructure (SS) replica of the main band CP (also,see Supplementary Figure). Their isotope shift (about 26meV) isan order of magnitude smaller than that of the IP at higher energy.Clearly, this strongly energy-dependent isotope effect cannot beascribed to an overall spectral shift or be described by the Migdal–Eliashberg theory. The increase of the spectral shift with increasingbinding energy suggests that the multi-phonon effect18,19 contrib-utes to the electron self energy up to very high energy20. Again, wenote that in the high-energy regime not only the electron–electroninteraction21,22 but also the electron–phonon interaction23 affect theelectron dynamics.

The inset of Fig. 2a summarizes the momentum dependence ofhigh-energy isotope shift. The isotope-induced shift is plotted as afunction of the superconducting gap. The linear correlation suggestsa strongly anisotropic isotope effect, which increases as the electronmomentum approaches the antinodal region.

In Fig. 2d, we show the dispersion for a cut parallel to the M–Ydirection, determined from the EDC peak position. The location ofthis cut is shown as cut 7 in the inset. As in Fig. 2a, it is remarkablethat, the higher the binding energy is, the stronger is the isotopeeffect. As the bottom of the dispersion is reached (yellow-filledcircles), an isotope shift (about240meV) nearly 20% of the entirewidth of the dispersion is observed (see arrows). The increase of theshift is consistent with Fig. 2a inset.

An additional important point is the isotope effect on thesuperconducting gap, Dk (see, for example, cuts 3–6 in Fig. 2a).Unlike the sample-independent, reproducible and reversible isotopeeffect at energies much larger than the gap energy, the changes of thesuperconducting gap are small and random in both magnitude andsign. In particular, the maximum value of the gap varies by about^5meV from one sample to another, regardless of the isotopemass.This suggests that the main cause of gap modification is disorder24,not the change in isotope mass. This is very different from thebehaviour of conventional s-wave superconductors25.

In Fig. 3, we study the effect of isotope substitution above thesuperconducting transition temperature (T ¼ 100K). Figure 3ashows the MDC dispersions along cuts 1 and 3–6 of Fig. 2a.Comparing Fig. 3a with Fig. 2a, we note an overall decrease of theisotope-induced changes. For example, in the antinodal region (thatis, cuts 5 and 6) the isotope effect is markedly different below andaboveT c, consistent with the rawMDCs and EDCs in Fig. 3b, c. Thisinteresting finding—that the strength of electron–lattice interactionis strongly temperature dependent—invalidates previous assump-tions9,10,15 that a strong temperature dependence of spectroscopicfeatures rules out phonons as explanation. As the last detailed point,we note that the sign reversal of the high-energy isotope effect nearcut 3 persists at high temperature, despite the reduced overallisotope effect.

Before discussing the implications of our results, we address twopossible sources of experimental error: unintentional dopingchange induced by the substitution process, and sample misalign-ment. Both of them are ruled out by the temperature dependenceand by the reversibility and the reproducibility of the observedeffects upon repeated measurements. Two more arguments can beused to rule out doping differences (also, see SupplementaryFigure). First, a direct comparison with the MDC dispersion atdifferent doping shows that the sign reversal at high energy cannotbe induced by a doping change. Second, if the changes in the high-energy nodal dispersions in Fig. 1 are due to a doping change Dx,Dx < 0.05 (ref. 11) is implied, which is five times bigger than themaximum doping uncertainty (Dx < 0.01) of the isotope substi-tution process.

A potentially simple explanation of our findings is the effect of

static lattice distortion, induced by the isotope substitution. How-ever, it is unlikely that the small change in the oxygenmass can affectthe overall lattice structure, as shown by diffraction results forLa22xSrxCuO4 (ref. 26). Moreover, the fact that the isotope effectsoccur with opposite signs for different cuts in momentum spaceexcludes a net average lattice change as explanation. Finally, theisotope substitution might induce a random static structuraldisorder, connected with the disorder seen in scanning tunnellingmicroscopy24. However, whereas the observed fluctuation of thesuperconducting gap is consistent with this possibility, the largerand fully reproducible isotope-induced changes at high energy arenot.On the basis of these findings we propose the following model for

the nature of electron–lattice coupling in high-T c superconductors.The fact that the isotope effect on the ARPES spectral functionbecomes much stronger below T c suggests a picture where pairingof electrons enhances their coupling to the lattice and vice versa, asin spin-Peierls physics2. In this picture, the motion of electron pairsmodifies the lattice distortion locally. If the coupling between theelectron pair and the lattice is too strong, the pair will be localizedand the lattice distortion becomes static. In that limit, the systembecomes an insulator rather than a superconductor. In the inter-esting situation where the coupling is not that strong, the dynamicspin-Peierls distortion follows the coherent motion of electron pairsin a superconducting state. Creation of a photo-hole in this state

Figure 3 Decrease of the isotope-induced changes in the normal state. The samples, the

k-axis definition, and the location of the cuts are identical to those in Fig. 2. a, Normal

state MDC dispersions for cuts parallel to theG–Y direction, fromG–Y to near the M point,

measured at T ¼ 100 K. A different origin of the momentum axis is used for each cut for

easy viewing of all data. b, Comparison of the isotope-induced changes of the raw MDCs

measured at 100 K and 25 K. The MDCs are measured at 200 meV binding energy for cut

6, as shown by the horizontal dashed line in a. c, Comparison of the isotope-induced

changes of the raw EDCs, at 100 K and 25 K. The momentum value for the EDCs

corresponds to the yellow-filled circle in the inset. As in Fig. 2c, a small peak near the

Fermi energy (0) due to the well-known superstructure (SS) replica (also, see

Supplementary Figure) coexists with the larger peak at high energy due to the main band

(MB). An apparent isotope-induced change of the height of the SS peak at 25 K is merely

due to the change of the position of the MB peak. All panels show that the isotope-induced

changes are reduced greatly at high temperature, except for near the nodal direction.

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causes the lattice to lose its distortion, and a strong couplingbetween the hole and the lattice results. Extrapolating this picture,we expect the diminishing of the spin-Peierls distortion above thepseudogap temperature T* (note that T* ¼ T c for optimally dopedBi2212). As a result, the coupling between the photo-hole and thelattice is weakened. The observation of significant isotope depen-dences of T* (refs 27), J and various low-temperature spin proper-ties28,29 supports this scenario.We believe that the above cooperativeinterplay between electron pairing and electron–lattice interactionoutlines the role that phonons play in high-temperature supercon-ductivity. The above proposal has been shown theoretically to workin one dimension30 and in a two-leg Hubbard ladder incorporatingthe electron–phonon interaction (A. Seidel, H. H. Lin and D.-H.L.,manuscript in preparation). A

Received 1 April; accepted 7 June 2004; doi:10.1038/nature02731.

1. Franck, J. P. in Physical Properties of High Temperature Superconductors IV (ed. Ginsberg, D. M.)

189–293 (World Scientific, Singapore, 1994).

2. Pytte, E. Peierls instability in Heisenberg chains. Phys. Rev. B 10, 4637–4642 (1974).

3. Muller, K. A. On the oxygen isotope effect and apex anharmonicity in high-Tc cuprates. Z. Phys. B 80,

193–201 (1990).

4. Bianconi, A. et al.Determination of the local lattice distortions in the CuO2 plane of La1.85Sr0.15CuO4.

Phys. Rev. Lett. 76, 3412–3415 (1996).

5. Gweon, G.-H., Zhou, S. Y. & Lanzara, A. Strong influence of phonons on the electron dynamics of

Bi2Sr2CaCu2O8þd. J. Phys. Chem. Solids (in the press).

6. Lanzara, A. et al. Evidence for ubiquitous strong electron-phonon coupling in high-temperature

superconductors. Nature 412, 510–514 (2001).

7. Allen, J. W., Gweon, G.-H., Claessen, R. & Matho, K. Fermi liquids and non-Fermi liquids—The view

from photoemission. J. Phys. Chem. Solids 56, 1849–1853 (1995).

8. Bogdanov, P. V. et al. Evidence for an energy scale for quasiparticle dispersion in Bi2Sr2CaCu2O8. Phys.

Rev. Lett. 85, 2581–2584 (2000).

9. Kaminski, A. et al. Renormalization of spectral lineshape and dispersion below Tc in

Bi2Sr2CaCu2O8þd. Phys. Rev. Lett. 86, 1070–1073 (2001).

10. Johnson, P. D. et al. Doping and temperature dependence of the mass enhancement observed in the

cuprate Bi2Sr2CaCu2O8þd. Phys. Rev. Lett. 87, 177007–177010 (2001).

11. Zhou, X. J. et al. Universal nodal Fermi velocity. Nature 423, 398 (2003).

12. Sato, T. et al. Observation of band renormalization effects in hole-doped high-Tc superconductors.

Phys. Rev. Lett. 91, 157003 (2003).

13. Eliashberg, G. M. Interactions between electrons and lattice vibrations in a superconductor. Zh. Eksp.

Teor. Fiz. 38, 966–976 (1960); Sov. Phys. JETP 11, 696–702 (1960).

14. Verga, S., Knigavko, A. & Marsiglio, F. Inversion of angle-resolved photoemission measurements in

high-Tc cuprates. Phys. Rev. B 67, 054503 (2003).

15. Hwang, J., Timusk, T. & Gu, G. D. High-transition-temperature superconductivity in the absence of

the magnetic-resonance mode. Nature 427, 714–717 (2004).

16. Rotenberg, E., Schaefer, J. & Kevan, S. D. Coupling between adsorbate vibrations and an electronic

surface state. Phys. Rev. Lett. 84, 2925–2928 (2000).

17. Cuk, T. et al. Coupling of the B1g phonon to the anti-nodal electronic states of

Bi2Sr2Ca0.92Y0.08Cu2O8þd. Preprint condmat/0403521 at khttp://xxx.lanl.govl (2004); Phys. Rev. Lett.(submitted).

18. Zhao, G. M., Hunt, M. B., Keller, H. &Muller, K. A. Evidence for polaronic supercarriers in the copper

oxide superconductors La2-xSrxCuO4. Nature 385, 236–240 (1997).

19. Crespi, V. H. & Cohen, M. L. Anharmonic phonons and the anomalous isotope effect in La2-

xSrxCuO4. Phys. Rev. B 44, 4712–4715 (1991).

20. Sawatzky, G. A. Testing Fermi liquid models. Nature 342, 480–481 (1989).

21. Shen, Z.-X. & Schrieffer, J. R. Momentum, temperature, and doping dependence of photoemission

lineshape and implications for the nature of the pairing potential in high-Tc superconducting

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22. Norman, M. R. et al. Unusual dispersion and line shape of the superconducting state spectra of

Bi2Sr2CaCu2O8þd. Phys. Rev. Lett. 79, 3506–3509 (1997).

23. Paci P. et al. Polaronic and nonadiabatic phase diagram from anomalous isotope effects. Preprint

condmat/0405053 at khttp://xxx.lanl.govl (2004).24. Pan, S. H. et al. Microscopic electronic inhomogeneity in the high-Tc superconductor

Bi2Sr2CaCu2O8þd. Nature 413, 282–285 (2001).

25. Anderson, P. W. Theory of dirty superconductors. J. Phys. Chem. Solids 11, 26–30 (1959).

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Supplementary Information accompanies the paper on www.nature.com/nature.

Acknowledgements We are grateful to K. A. Muller, A. Bianconi, N. L. Saini, D. Pines, A. Bill,

V. Z. Kresin, S. A. Kivelson, A. J. Leggett, J. Clarke, J. Orenstein, M. L. Cohen, L. Pietronero,

E. Cappelluti, J. C. Davis, J. W. Allen, A. S. Alexandrov, J. C. Phillips, A. H. Castro Neto,

C. Castellani, A. Bussman Holder, D. Mihailovic, G. Deutscher, C. Bernhard, S. Uchida and

T. Schneider for discussions. We thank Z. X. Shen, Z. Hussain, D. S. Chemla and N. V. Smith for

support in the initial stage of the project. The work at UC Berkeley and LBNLwas supported by

the Department of Energy’s Office of Basic Energy Science, Division of Materials Science.

Competing interests statement The authors declare that they have no competing financial

interests.

Correspondence and requests for materials should be addressed to A.L. ([email protected]).

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Colloidal nanocrystalheterostructures with linearand branched topologyDelia J. Milliron1,2, Steven M. Hughes1,2, Yi Cui1,2, Liberato Manna1,2*,Jingbo Li3, Lin-Wang Wang3 & A. Paul Alivisatos1,2

1Department of Chemistry, University of California, 2Materials Science Division,and 3Computational Research Division, Lawrence Berkeley National Laboratory,Berkeley, California, 94720, USA

* Present address: National Nanotechnology Lab of INFM, Via Arnesano, 73100 Lecce Lecce, Italy

.............................................................................................................................................................................

The development of colloidal quantum dots has led to practicalapplications of quantum confinement, such as in solution-processed solar cells1, lasers2 and as biological labels3. Furtherscientific and technological advances should be achievable ifthese colloidal quantum systems could be electronically coupledin a general way. For example, this was the case when it becamepossible to couple solid-state embedded quantum dots intoquantum dot molecules4,5. Similarly, the preparation of nano-wires with linear alternating compositions—another form ofcoupled quantum dots—has led to the rapid development ofsingle-nanowire light-emitting diodes6 and single-electron tran-sistors7. Current strategies to connect colloidal quantum dots useorganic coupling agents8,9, which suffer from limited control overcoupling parameters and over the geometry and complexity ofassemblies. Here we demonstrate a general approach for fabri-cating inorganically coupled colloidal quantum dots and rods,connected epitaxially at branched and linear junctions withinsingle nanocrystals. We achieve control over branching andcomposition throughout the growth of nanocrystal heterostruc-tures to independently tune the properties of each componentand the nature of their interactions. Distinct dots and rods arecoupled through potential barriers of tuneable height and width,and arranged in three-dimensional space at well-defined anglesand distances. Such control allows investigation of potentialapplications ranging from quantum information processing toartificial photosynthesis.

Unlike vapour–liquid–solid (VLS)- or SLS-grown nanowires,anisotropic nanocrystals in homogeneous solutions grow withoutthe benefit of catalyst activation of one end. Hence, heterostructuregrowth in colloidal nanocrystals has so far been limited to core–shellstructures that serve primarily to further isolate quantum dots fromtheir environment10,11,12,13,14. An elegant extension of core–shellgrowth enabled concentric alternating layers of CdS and HgS,which have a type I (nested) band alignment15,16. Control over theelectronic structure of concentric heterostructures is, however,restricted by their simple geometry and by strain due to latticemismatch, which typically limits the thickness of each layer to a fewmonolayers or less. Heterostructures based on nanorods permit

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Chapter 5

The bond stretching phonon

dispersion

In Ref. [9], we report for the rst time the phonon dispersion relation ina single layer Bi-cuprates superconductors using inelastic x-ray scattering.In particular we study the momentum dependence of the highest opticalphonon, the bond stretching phonon, widely discussed in the literature ofother cuprates because of the presence of an anomalous softening at a char-acteristic wave vector qc=0.25-0.3. We found that the same mode undergoesa softening, accompanied by an anomalous broadening of the line width,similar to the one reported in other cuprates at a comparable q vector. Bycombining the result of IXS with ARPES measurements on the same samplewe could get a unique insight on the role that this phonon plays in the de-termining the dressing of quasiparticles at low energy in single layer Bi2201.More specically we discovered the presence of two kinks in the ARPES spec-tra occurring at dierent energies (63meV vs 35meV) and in dierent regionsof the momentum space (nodal region vs antinodal region). The comparisonwith the IXS data allows to identify the kink in the nodal region with thesoft part of the bond stretching phonon. These two new results combined to-gether provide unprecedented support for the lattice origin of the kink in theelectronic structure of the cuprates high temperature superconductors and inaddition reveal an unexpected complex interaction between the length of theFermi arcs, the kink in the electronic dispersion and the phonon anomaly.

Moreover, the combination of these two experimental probes added a newpiece of information to the physics of cuprates, e.g. a link between the Fermiarcs length, the phonon energy scale and identify the tip of the Fermi arcs asthe point where new bosonic excitation comes into play. This is of particularinterest in the light of the recent breakthroughs connecting the Fermi arcsregion with the true superconducting gap [30, 31].

46 The bond stretching phonon dispersion

To address the question whether this energy scale observed in both IXSand ARPES is a signature of a lattice driven stripe phase, as discussed inthe literature [81], we performed high resolution IXS studies on In the sec-ond letter (physical review B), we investigated in more detail the the latticedynamics of underdoped La2−xSrxCu2O4, and in particular the anomalousbroadening of the BS phonon. The very high intrinsic Q resolution of inelas-tic x-ray scattering allows to disentangle the possible dispersion eect fromintrinsic broadening due to reduced phonon lifetime. This is very critical,since we argue that the broadening is related to a strong electron phonon in-teraction in the rst letter. Our results suggest that the broadening alreadyreported for q=0.25, is intrinsic, and not due to a fast dispersion.

Bond stretching phonon softening and angle-resolved photoemission kinks inoptimally doped Bi2Sr1.6La0.4Cu2O6+δ superconductors

J. Graf,1 M. d’Astuto,2 C. Jozwiak,3 D.R. Garcia,1, 3 N. L. Saini,4 M.Krisch,5 K. Ikeuchi,6 A.Q.R. Baron,7 H. Eisaki,8 and A. Lanzara1, 3, ∗

1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA2Institut de Mineralogie et de Physique des Milieux Condenses (IMPMC),

Universite Pierre et Marie Curie - Paris 6, case 115, 4, place Jussieu, 75252 Paris cedex 05, France†3Department of Physics, University of California Berkeley, CA 94720, USA

4Dipartimento di Fisica, Universita di Roma La Sapienza, 00185 Roma, Italy5European Synchrotron Radiation Facility, F-38043 Grenoble Cedex, France

6SPring-8/JAEA,1-1-1 Kouto, Sayo, Hyogo, 670 Japan7SPring-8/RIKEN&JASRI, 1-1-1 Kouto, Sayo, Hyogo, 670 Japan

8AIST Tsukuba Central 2, Umezono, Tsukuba, Ibaraki, 305-8568, Japan(Dated: March 10, 2008)

We report the first measurement of the optical phonon dispersion in optimally doped single layerBi2Sr1.6La0.4Cu2O6+δ using inelastic x-ray scattering. We found a strong softening of the Cu-O bondstretching phonon at about q = (≈ 0.25, 0, 0) from 76 to 60 meV, similar to the one reported in othercuprates. A direct comparison with angle-resolved photoemission spectroscopy measurements takenon the same sample, revealed an excellent agreement in terms of energy and momentum betweenthe ARPES nodal kink and the soft part of the bond stretching phonon. Indeed, we find that themomentum space where a 63±5 meV kink is observed can be connected with a vector q = (ξ, 0, 0)with ξ ≥ 0.22, which corresponds exactly to the soft part of the bond stretching phonon mode. Thisresult supports an interpretation of the ARPES kink in terms of electron-phonon coupling.

The coupling of electrons to phonons can be studiedfrom the renormalization of the phonon dispersions usingboth inelastic neutron (INS) and x-ray scattering (IXS).For example, if the phonon wavevector matches 2kF ,where kF is the Fermi momentum, an enhancement ofthe electron-phonon coupling occurs due to Fermi surfacenesting, resulting in phenomena such as Kohn anomalyor charge density wave. Similarly, the coupling of elec-trons to thermal excitations as phonons or magnons ismanifested in ARPES data by a kink in the electronicdispersion near the excitation frequency [1]. Hence a fullmapping of both electron and phonon dispersion is fun-damental to uncover the electron-phonon interaction ina material.

INS and IXS data have shown an anomalous softeningof the Cu-O bond stretching (BS) mode at the metal-insulator phase transition in several cuprates supercon-ductors [2–9] as well as non-superconducting perovskites[7, 10, 11]. Whether this anomalous softening is relatedto superconductivity or to the strong charge order insta-bilities present in some of these compounds is not clearyet, since neither of these two phenomena are ubiquitousto all of these compounds.

ARPES data have shown a kink in the electronic dis-persion at 60-70 meV along the nodal direction in vari-ous p-type cuprates [12]. This kink shifts toward lowerbinding energy (30-40 meV) as the Brillouin zone face isapproached [13–15]. Due to the coinciding energy, thenodal kink has been associated with the BS phonon [12].However, an alternative explanation has been suggested[16, 17]. Therefore, what is the true nature of the nodal

kink, what determines the momentum region where it ex-ists and what are the signatures of the anomalous phononsoftening on the electronic structure are still open ques-tions.

A combination of IXS and ARPES measurements onthe same material is therefore very valuable in establish-ing, if any, the exact relation between these two anoma-lous behaviors. Such a study has been missing so far.The best system to perform this cross analysis is the sin-gle layer Bi2Sr1.6La0.4Cu2O6+δ superconductor (Bi2201)as no report of a magnetic resonance mode exists, allow-ing one to draw a direct comparison between the elec-tronic structure and the phonon spectra. Also, the Bi-based cuprates are among the most studied materials byARPES because of the good quality of their cleaved sur-face. On the other hand, the lack of large single crystalshas made INS experiment difficult and, though IXS canprobe sub-millimeter crystals, this is a challenging exper-iment due to the very low inelastic cross section of theBS mode [18].

We report the first measurements of the dispersion ofthe longitudinal phonons in optimally doped Bi2201. Wefind a strong anomaly and renormalization of the BSphonon dispersion along the q = (ξ, 0, 0) direction, sim-ilar to the one reported in several cuprates [2–5, 7, 8].ARPES measurements revealed the presence of two dis-tinct kink structures near the node and the BZ face at60-70 and 30-40 meV respectively, similar to the two kinkstructure reported in double layer Bi2Sr2CaCu2O8+δ

[13, 14] and La2−xSrxCu2O4 [15].

From the comparison between ARPES and IXS mea-

2

FIG. 1: IXS phonon spectrum of Bi2201 at 10K. The markersare the raw data, the dashed line is the resolution function andthe plain line is a fit. (a) Low energy part of the spectrum.(b) High energy part with a smaller y-scale.

surements performed on the same sample, we show thatthe soft part of the BS phonon matches the energy andmomentum of the 60-70 meV kink.

The single crystals of Bi2201 (Tc=33 K) were grownusing the traveling-solvent floating-zone technique [19].The IXS experiment was performed at beamline BL35XUat SPring-8 in Japan [20] and completed at beamlineID28 at the European Synchrotron Radiation Facility inFrance [21]. The momentum and energy resolutions werebetter than 0.08 A−1 and 3.2 meV respectively. Themeasurements were done in the transmission geometryat low temperature (≈10 K) to reduce contribution fromthe low energy phonons peaks. The sample thickness was≈ 30µm, allowing ≈ 30% of x-ray transmission.

IXS energy scans were carried out at Q = G + qpoints of the reciprocal lattice, where G is the zone cen-ter vector, and q is the reduced vector which correspondsto the phonon propagation vector. The exact Q pointsare: Q=(3.02,0,0.18),(3.09,0,0.06),(3.15,0,-0.06),(3.22,0,-0.19) at SPring8 and Q=(3.25,0,0),(3.45,0,0) at ESRF.For the rest of the paper, we will neglect the c-axiscomponent of the momentum transfer since the phononanomaly was found to be independent of the c-component[22]. The six Q points will be described by the reducedvector q = (ξ, 0, 0).

The ARPES experiments were carried out at beam-line V-4 of the Stanford synchrotron radiation laboratorywith 22.4 eV photon. The ARPES data along the nodewere reproduced using an in-house 6 eV laser-based setupsimilar to the one described in ref. 23. In both case thetotal energy and angular resolution were better than 14meV and 0.4, respectively and the sample temperaturewas bellow 15 K.

Fig. 1 shows a typical IXS energy-scan in longitu-dinal geometry at Q=(3.02,0,0). A harmonic oscillatorconvoluted with the instrumental resolution function wasused for the fit. Three features can be clearly distin-

FIG. 2: (Color online) LO phonons dispersion. (a) IXS spec-tra for Q=(3+ξ,0,0) with ξ spanning from the BZ center(top spectrum, ξ = 0.02) to the BZ face (bottom spectrum,ξ = 0.45). The spectra are vertically shifted. The plain linesshow the harmonic oscillator fit, the dashed lines show theelastic tail and the dotted lines show the last two mode usedin the fit. (b,c) Phonon dispersions. The cosine dashed linesare guides for the eyes illustrating the crossing (b) and anti-crossing (c) scenarios. (d) FWHM. The error bars are anestimate of the standard deviation of the fit coefficients

guished in panel (a): (I) the elastic peak at 0 meV is thestatic diffuse scattering coming from disorder or weaklyordered structures; (II) the first longitudinal acousticphonon centered around 6 meV and (III) two low energyoptical modes at 14 and 21 meV. Other phonon modesare not resolved due to the dominating contribution fromthe tails of the elastic and acoustic signals. Panel (b)shows the same energy scan at higher energy. The smallerror bars above 50 meV reflect the very good statisticalquality of the data. Two peaks corresponding to the lasttwo longitudinal optical (LO) phonon modes are clearlyresolved in the data.

Fig. 2 shows the evolution of these two highest LOphonons across the Brillouin zone (BZ). Panel (a) showsthe IXS spectra for ξ spanning from the BZ center to theBZ face. At the BZ center, two peaks are resolved. Thefirst peak is at 58 meV and the second is at 76 meV. Bothare almost resolution limited. As we approach the zoneface, both peaks disperse toward 65 meV and as ξ reaches0.22-0.25, the two modes are not distinguishable despitethe very good energy resolution used here. The ξ=0.25spectrum shows actually a rather ill-defined broad peak,extending far in the low energy side. For ξ=0.45 we canresolve again two sharp peaks.

In panel (b) and (c), we show the dispersion of the two

3

FIG. 3: (Color online) (a) Dispersion of the BS mode forvarious optimally p-doped single layer cuprates in comparisonwith the Bi2201 data. The frequencies are normalized to theirvalue at ξ = 0. The error bars are an estimate of the standarddeviation of the fit coefficients. The optimally doped LSCOand LaBaCuO are from [22] and the Hg1201 are from [3]. (b)FWHM when available.

branches across the BZ. There are two likely scenariosdepending on the symmetry of the two branches. If theyhave the same symmetry, they anti-cross, otherwise theysimply cross. The dashed lines are guides for the eyesused to illustrate the crossing (b) and the anti-crossing(c) scenarios. In the case of an anti-crossing, the char-acter of the two modes are exchanged between the twobranches at the anti-crossing point. Therefore in eithercase, the 60 meV peak at ξ=0.45 has the character of theCu-O BS mode, leading to a total softening of 16 meV.A similar anti-crossing phenomenon is observed in then-doped cuprate Nd1.86Ce0.14CuO4+δ [5, 24] where theCu-O BS mode anti-crosses with the Nd-O BS mode. Inthe case of optimally doped La2−xSrxCu2O4 (LSCO), amode with little dispersion is seen at the same energy,58 meV and has been attributed to the O bond bendingmode [6].

In order to distinguish between the two scenarios, weundertook conventional phonon calculations using a clas-sical shell model [25]. The parameters used are based onthe model from ref. [26]. This model did not reproducethe low and high energy modes observed experimentallyin a reliable way. This indicates that spectral ellipsome-try data alone could not provide enough constraints forthe parameters of the model. All our attempts to finda better set of potentials compatible with previous es-tablished potential sets [27] failed. Several factors mightbe responsible for such disagreement, including: (I) thecharge distribution and bonds of the high Z atoms con-taining f electrons (Bi) are very difficult to model accu-rately [28], and (II) the one-dimensional incommensuratesuperstructure along the b-axis [29] which is neglected inthe calculation.

Panel (d) shows the corresponding FWHM of eachpeak. The two modes are sharp and almost resolu-tion limited across the whole BZ except for ξ=0.22-0.25,where only one broad peak is resolved.

Fig. 3 shows a comparison of the Cu-O BS phonondispersion (a) and FWHM (b) for various optimally p-

FIG. 4: (a) Electron energy vs momentum dispersion rela-tion measured by ARPES for three different momentum cuts.Cut 1 is along the node and was measured with 22.4 eV syn-chrotron radiation (plain circles) and with 6 eV radiation us-ing a laser based setup (open circles). Cut 2,3 are furthertoward the BZ face, close to the edge of the Fermi arcs re-ported in pseudogap state [30]. Cut 2,3 were measured withsynchrotron light only. The spectra are shifted horizontallyand a ≈4 meV gap for cut 2,3 is subtracted. (b) Experimen-tal Fermi surface with the momentum location of the 3 cuts.The apparent finite Fermi arcs are due to the experimentalresolution. The plain line shows a constant energy contourat the kink energy, 63meV. The inset of panel (b) shows theIXS dispersion and peak FWHM (error bars) of the BS modediscussed above. The shadow area represents the nodal kinkenergy and the Q vectors connecting the Fermi surface seg-ments where the nodal kink is observed. Note that ξ=0.2corresponds to 0.4 ∆kx (π/a).

doped single layer cuprates. For Bi2201, an additionaldata point at ξ ≈0.3 is still needed to establish experi-mentally the exact momentum value of the maximal soft-ening, though these data already suggest that the maxi-mum FWHM is observed around ξ ≈0.22-0.25 in agree-ment with other cuprates [24]. We note however thatthe softening in the Bi2201 dispersion is smoother andobservable already at very low ξ in contrast with othercuprates.

In Fig. 4, we compare the IXS and ARPES resultsfor the phonon and electron dispersions in Bi2201. Panel(a) shows the energy momentum dispersion relation nearthe Fermi energy measured by ARPES along the nodaldirection from the node to the BZ face. The exact mo-mentum location of the cuts is shown in panel (b). Inagreement with previous reports, we observe a kink at63±5 meV along the nodal direction (cut 1). For cut 2,we observe in addition to the kink at 63meV, a kink at35meV. For cut 3, we observe only the kink at 35 meV.The kink positions were extracted using a two straightlines fit [12]. Different methods including the analysis ofthe self energy [31] and of the first derivative of the dis-persion (not shown) provided the same kink positions. Asimilar shift of the kink toward lower binding energy hasbeen reported for other cuprates [13–15]. The momen-tum where the 63 meV kink disappears seems to coincide

4

with the tip of the Fermi arcs determined from the hightemperature data [30]. In this paper we will refer to thelength of the Fermi arcs as determined from data in thepseudogap phase [30].

The direct comparison with the dispersion of the BSphonon clearly shows that the energy of the 63 meVkink coincides with the energy of the soft part of the BSphonon. To extend the comparison also to the momen-tum space we show in panel (b) a constant energy mapof ARPES spectral intensity vs momentum at the Fermienergy (Fermi surface) in the superconducting state anda constant energy contour (gray line) at the nodal kinkenergy (63meV).

The comparison between the momentum of the BSphonon and the constant energy maps can provide uniqueinformation on the wavevectors needed for the electronsat the nodal kink to be scattered to the Fermi level bythis particular phonon. The gray shadow area representsthe range of q=(ξ,0,0) vectors that connect the electronicexcitations at the 63meV kink energy (grey closed con-tour) to the Fermi surface segments from the node tothe BZ face at the locations where the nodal kink is ob-served. For clarity the gray area is shown only for halfof a Fermi arc, but the same construction can be appliedto the entire Fermi arc by symmetry.

We find that the entire momentum region where weobserve a 63 meV kink can be connected with a momen-tum transfer q=(ξ,0,0) or equivalently q=(0,ξ,0) withξ ≥ 0.22 to an opposite, quasi-parallel Fermi surface seg-ment. This momentum transfer corresponds exactly tothe momentum region where the Cu-O BS phonon showsa softening and an anomalously broad lineshape (illus-trated with the large error bars in the inset of panel (b)).Note that the furthest tips of the Fermi surface arcs areconnected by q=(0.5,0,0) which still corresponds to thesoft BS mode. However, because of the relative orien-tation of these Fermi arcs (the momentum transfer isalmost parallel to the Fermi arcs), the coupling with aperpendicular phonon (q=(0,0.22,0)) is expected to bestronger. Interestingly, the maximum broadening corre-sponds to the case in which the momentum transfer isalmost perpendicular to the Fermi arcs, suggesting thatthe anomalous softening and broadening observed in thephonon spectra might be a consequence of this Fermi sur-face topology. A similar study with a doping dependencecould confirm this scenario. An analogous scenario mayapply to the 35meV mode as well, but a more extensiveIXS data set is required to confirm this.

The BS mode is supposed to be non-dispersive at about80 meV along the other directions and in particular along[110] for the full breathing mode [2, 22, 24]. The absenceof any strong feature above 63 meV in the ARPES datashows that the nodal charge carriers are preferentiallycoupled with the soft Cu-O half-breathing BS mode dis-persing along the [100] direction as suggested by recentLSDA+U results [32].

In conclusion, we report the first evidence of ananomalous dispersion of the Cu-O bond stretchingphonon mode in a Bi-cuprate. A direct comparisonwith ARPES data shows that the energy and momentumwhere the strongest coupling to a 63 meV mode is ob-served corresponds exactly to the energy and momentumof the soft and broad Cu-O BS phonon. Considering thata magnetic resonance mode was never observed in singlelayer Bi2201 [33], this result provides a strong support forthe lattice origin of the 60-70 meV ARPES nodal kink.Although the role of electron-phonon coupling for super-conductivity is not known yet, it is beyond any doubtthat it is an important interaction linked with the Fermisurface topology, and it should not be neglected in anyrealistic theory of cuprates.

We thank D. Reznik and D.-H. Lee for useful discus-sions. The ARPES measurements were supported bythe Division of Materials Sciences and Engineering, Of-fice of Basic Energy Sciences of the U.S. Department ofEnergy under Contract No. DE-AC03-76SF00098. TheIXS measurements were equally supported by the France-Berkeley grant, the Division of Materials Sciences andEngineering, Office of Basic Energy Sciences of the U.S.Department of Energy under Contract No. DE-AC03-76SF00098 and by the by the National Science Founda-tion through Grant No. DMR-0349361.

∗ Electronic address: [email protected]† Institut de Mineralogie et de Physique des Milieux Con-

denses (IMPMC), CNRS UMR 7590, Campus Boucicaut,140 rue de Lourmel, 75015 Paris, France

[1] N. W. Ashcroft, N. D. Mermin, Solid State Physics(Brooks Cole, 1976).

[2] L. Pintschovius, et al., Phys. B 174, 323 (1991).[3] H. Uchiyama, et al., Phys. Rev. Lett. 92, 197005 (2004).[4] N. Pyka, et al., Phys. Rev. Lett. 70, 1457 (1993).[5] M. d’Astuto, et al., Phys. Rev. Lett. 88, 167002 (2002).[6] R. J. McQueeney, et al., Phys. Rev. Lett. 82, 628 (1999).[7] D. Reznik, et al., Nature 440, 1170 (2006).[8] J.-H. Chung, et al., Phys. Rev. B 67, 014517 (2003).[9] L. Pintschovius, M. Braden, Phys. Rev. B 60, R15039

(1999).[10] L. Pintschovius, et al., Phys. Rev. B 40, 2229 (1989).[11] W. Reichardt, M. Braden, Phys. B 263-264, 416 (1999).[12] A. Lanzara, et al., Nature 412, 510 (2001).[13] T. Cuk, et al., Phys. Rev. Lett. 93, 117003 (2004).[14] A. D. Gromko, et al., Phys. Rev. B 68, 174520 (2003).[15] K. Terashima, et al., Phys. Rev. Lett. 99, 017003 (2007).[16] P. D. Johnson, et al., Phys. Rev. Lett. 87, 177007 (2001).[17] A. Kaminski, et al., Phys. Rev. Lett. 86, 1070 (2001).[18] M. d’Astuto, et al., Phys. B 316-317, 150 (2002).[19] H. Eisaki, et al., Phys. Rev. B 69, 064512 (2004).[20] A. Q. R. Baron, et al., J. Phys. Chem. Solids 61, 461

(2000).[21] M. Krisch, et al., Phys. Rev. B 65, 134201 (2002).[22] D. Reznik, et al., J. Low Temp. Phys. 147, 353 (2007).[23] J. D. Koralek, et al., Phys. Rev. Lett. 96, 017005 (2006).

5

[24] M. Braden, et al., Phys. Rev. B 72, 184517 (2005).[25] http://sourceforge.net/projects/openphonon (2001).[26] N. N. Kovaleva, et al., Phys. Rev. B 69, 054511 (2004).[27] S. L. Chaplot, et al., Phys. Rev. B 52, 7230 (1995).[28] B. Renker, H. Schober, F. Gompf, J. Low Temp. Phys.

105, 843 (1996).[29] M. D. Kirk, et al., Science 242, 1673 (1988).

[30] T. Kondo, et al., Phys. Rev. Lett. 98, 267004 (2007).[31] S. Verga, A. Knigavko, F. Marsiglio, Phys. Rev. B 67,

054503 (2003).[32] P. Zhang, S. G. Louie, M. L. Cohen, Phys. Rev. Lett. 98,

067005 (2007).[33] T. Sato, et al., Phys. Rev. Lett. 91, 157003 (2003).

In-plane copper-oxygen bond-stretching mode anomaly in underdoped La2−xSrxCuO4+ measuredwith high-resolution inelastic x-ray scattering

Jeff GrafMaterials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

Matteo d’Astuto,* Paola Giura, and Abhay ShuklaInstitut de Minéralogie et de Physique des Milieux Condensés (IMPMC), Université Pierre et Marie Curie-Paris 6, case 115, 4,

place Jussieu, 75252 Paris Cedex 05, France†

Naurang L. SainiDipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy

Alexei Bossak and Michael KrischEuropean Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex, France

Sang-Wook CheongRutgers Center for Emergent Materials and Department of Physics & Astronomy, Rutgers, Piscataway, New Jersey 08854, USA

Takao SasagawaDepartment of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 7-3-1 Hongo-Bunkyo, Japan

Alessandra LanzaraMaterials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

and Department of Physics, University of California Berkeley, California 94720, USAReceived 25 July 2007; published 27 November 2007

We have measured the lattice dynamics of underdoped La2−xSrxCuO4+ x=0.08 using high resolutioninelastic x-ray scattering spectroscopy. The very good intrinsic Q resolution of this experiment allows us todifferentiate between the two proposed scenarios for the Cu-O bond stretching phonon broadening reported atq= 0.25,0 ,0. The results suggest that this phonon broadening is due to intrinsic damping rather than to asteep dispersion, having important implications on the interpretation of phonon anomalies in cuprates.

DOI: 10.1103/PhysRevB.76.172507 PACS numbers: 74.72.Dn, 63.20.Kr, 63.20.Dj, 74.25.Kc

Doping related anomalies in the high-energy longitudinaloptical branch of the transition metal-oxygen bond-stretchingBS mode are a general feature of perovskitelike transitionmetal oxides.1 In order to understand their possible relevanceto high-Tc superconductivity in cuprate and Ba1−xKxBiO3systems, they have been extensively investigated, mainly us-ing inelastic neutron scattering INS,2–4 and more recentlyusing inelastic x-ray scattering IXS.5,6

In particular, La2CuO4+ has been a model for these stud-ies. The first measurements of the Cu-O BS mode only re-ported a cosinelike dispersion,2 which can be easily under-stood in terms of conventional calculations.8 Subsequentmeasurements, however, pointed to anomalous behavior re-lated to charge inhomogeneities and three different interpre-tations have emerged. McQueeney and co-workers9 reporteda doubling of the unit cell in the 100 direction attributed toquasistatic charge stripes, i.e., with slower dynamics than theBS phonon frequency. Within this picture, a second phononmode appears at lower energy for q= ,0 ,0 with largerthan 0.25, when the system is doped. At q= 0.25,0 ,0where the softening occurs, the Cu-O bond stretching modeis weak and spread over a large energy window10–15 meV. A similar behavior has been seen for theBa1−xKxBiO3 Ref. 4 and the La2−xSrxNiO4 Ref. 10 along

the propagation vector for charge inhomogeneities in thesesystems. The results of McQueeney and co-workers9 havebeen later contradicted by Pintschovius and Braden,11 thatinterpreted their data differently. They find a smooth Cu-Obond stretching dispersion, with an anomalously high slopeand broadening around q= 0.25,0 ,0. More recently,Reznik and co-workers,7 proposed a third description for theanomaly around q= 1

4 ,0 ,0. In particular, by measuringLa2−xBaxCuO4, for x 1

8 where quasistatic stripes exist, theyreported a strong enhancement of the broadening and as-signed it to a sharp softening at the stripes propagation vec-tor q= 0.25,0 ,0. Based on this result, their conclusion wasthat the anomalies observed in other cuprates are merely areminiscence of this sharp softening, due to incipientdynamic stripes order.

To distinguish between these different scenarios a highresolution study of the high-energy longitudinal optical Cu-Obond stretching mode is needed. Here we report a high-resolution study of the phonon dispersion in an underdopedLa2−xSrxCuO4+ with x=0.08 by high-resolution inelasticx-ray scattering IXS spectroscopy. IXS easily allows us toachieve high Q resolution, thanks to the high brightness i.e.,high flux in a small emission angle, and for a small energybandwidth of the incoming beam together with a very small

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beam size. One can thus probe small crystals, for which highquality growth, with low mosaic and high homogeneity, iseasily obtained. The Q resolution is dominated by the angu-lar acceptance of the scattered x rays, while the energy reso-lution is constant, independent of the energy transfer andscattering vector in a large Q intervals. This implies that anenergy resolution of 5% or less can be achieved for phononenergies above 30 meV, and for a wide choice of scatteringvectors. Note that, underdoped La2−xSrxCuO4+ has alreadybeen measured using IXS by Fukuda and co-workers,12 butwith an energy resolution 7–8% of the energy transfer,comparable or even less than the one offered by conventionalinelastic neutron scattering INS experiments.

The experiment was carried out at the inelastic x-ray scat-tering beamline II ID28 at the European Synchrotron Ra-diation Facility in Grenoble. We studied a crystal ofLa2−xSrxCuO4+ with nominal doping x=0.08, grown using aflux method.13 Superconducting transition temperature Tc=21 K measured by superconducting quantum interferencedevice magnetometry is consistent with the nominal doping.The sample was mounted in reflection geometry on the coldfinger of a closed-loop helium cryostat. The c axis of thecrystal was perpendicular to the scattering plane, and weselected an almost single domain in our twinned samplethanks to the beam spot of hv0.30.1 mm. We con-sider the orthorhombic unit cell with ===90° and theaxes a and b along the Cu-O bond. The sample was alignedalong H ,0 ,0, and we refined the parameter a=3.794±0.001 Å, according to the -2 scan on the 4, 0, 0reflection, and adopted the value of c=13.2 Å. The rockingcurve at the 4,0,0 reflection had a full width at half maxi-mum FWHM 0.01° corresponding to a very small mosaicspread in a single domain probed by the beam. The IXSspectrometer14 configurations chosen were of the type G+q= 3,0 ,0+ , ,, with simultaneous measurementsfrom five analyzers in the plane perpendicular to the c axis=0 see, e.g., Ref. 15 for more details. In this setup, onlyone of the analyzers was in the exact longitudinal condition=0. We selected data taken from the analyzers in the posi-tions corresponding to 0.05, for the longitudinal spectra,

and a reference scan in transverse configuration with =0and =0.135. This setup corresponds to the third extendedBrillouin zone, where the zone center is at 4,0,0 and theextended zone boundary at 3,0,0. The standard or foldedzone boundary is at the point M = 3.5,0 ,0 in this Brillouinzone. The scattering vector resolution was set using a slitopening in front of the analyzers of hv=2060 mm cor-responding to a solid angle of =0.19° 0.57°. Thehigh-energy resolution is obtained using the high orderBragg reflections of type HHH of the backscattering siliconmonochromator.16 In the present experiment we have chosento work with the Si 9 9 9 reflection, with a wavelength of0.6968 Å 17794 eV and an energy resolution E=3.0±0.2 meV. Additional spectra were collected using theSi 8 8 8 reflection, with a wavelength of 0.7839 Å15816 eV and an energy resolution E=5.5±0.2 meV.The backscattered beam is focused on the sample position bya gold-coated toroidal mirror, which provides a focal spot ofhv=0.2700.090 mm FWHM. The resolution in the re-ciprocal space was ± ,0 ,0 with 0.009 for 0.6968 Åwavelength. Examples of raw IXS spectra are given in Fig. 1panel a for E=5.5±0.2 and b for E=3.0±0.2 meV.The energy scans were fitted using a sum of pseudo-Voigt

I1 − /2

− 02 + 2/4+ exp−

ln 2 − 02

2/4 ,

1

and Lorentzian functions

I/2

− 02 + 2/4, 2

where ==h is the phonon energy. Pseudo-Voigt func-tions were used to fit elastic and resolution-limited inelasticcontributions, with and parameters adapted to match theinstrumental function, while a Lorentzian line shape wasused to fit modes with an intrinsic width larger than the in-strumental resolution. Alternatively, a convolution with theexperimental resolution function was adopted. In this case,

FIG. 1. Representative energy scans below 20 K. Error bars represent ±1 s.d. a, b Inelastic x-ray scattering IXS energy scans takenon La1.92Sr0.08CuO4+ LSCO at T=16 K, with E=5.5±0.2 a and E=3.0±0.2 meV b. c Inelastic neutron scattering INS energyscans taken on La1.875Ba0.125CuO4 LBCO at T=10 K from Ref. 7. d Comparison of the BS mode fit of panel a and b. e Comparisonof the BS mode fit in LSCO E=3.0 meV and the BS mode fit in LBCO from Ref. 7.

BRIEF REPORTS PHYSICAL REVIEW B 76, 172507 2007

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the response function was composed of a sum of delta func-tions instead of pseudo-Voigts, plus a Lorentzian for themodes with an intrinsic width larger than the instrumentalresolution. The two data analysis procedures gave consistentresults. The fitting algorithm used a 2-minimization routine,and the detailed balance constrain between Stokes and anti-Stokes excitations constrain. A constant background, comingessentially from electronic noise, was added. In order to as-sign the measured phonon modes, we performed a latticedynamical calculation using a computer code17 based on theshell model. The set of atomic parameters was chosen ac-cording to the one obtained from a comparison of the INSresults for different HTS cuprates established by Chaplot andco-workers,18 as described in Ref. 5.

By fitting many experimental spectra such as the ones inFigs. 1a and 1b, we extracted the dispersion of the pho-non modes, and their relative intensities, as shown in Fig. 2.In this figure, data from two different experiments indicatedby solid gray or hatched black circles were analyzed inde-pendently and gave consistent results. In Fig. 1 our IXS en-ergy scans on La1.92Sr0.08CuO4+ are compared to INS spec-tra taken on La1.875Ba0.125CuO4 from Ref. 7 at similartemperature and q vectors. In Figs. 1a and 1b we can seethat the width of the highest energy LO mode changes toalmost a factor of 2 at =0.9, according to the change in theinstrumental function from Si 8 8 8 to 9 9 9 monochro-mator Bragg reflection. On the other hand, the width for =0.25 or equivalently 0.75 does not change notably, imply-ing that the intrinsic broadening derived by damping domi-nates. We note that the maximum width occurs for =0.75,consistent with previous measurements9,11,12 and in contra-diction with a picture in which the large broadening corre-sponds to the stripe q vector for x=0.08 the vector q wouldbe 0.16,0 ,0, as also pointed out in Ref. 7. Incidentally,we also note that the width, for =0.75 in Figs. 1a and1b, does not appear very different from the one in Fig.1c. This seems to contradict the argument that theLa1.875Ba0.125CuO4 system shows an enhanced broadening,compared to La1.92Sr0.08CuO4+, at q= 0.25,0 ,0 Ref. 7.

In Fig. 2 left panel, we show the dispersion of the lon-gitudinal and transverse in-plane phonon modes. Data pointsare obtained from the fits to the IXS data, as describedabove, and continuous lines from our lattice dynamical cal-culations. There is a good agreement of the measured andcalculated frequencies, except for the softening at about =0.75, which is consistent with the softening, observed inanother IXS study,12 in an underdoped La1.92Sr0.08CuO4+.Note that the dashed bars on the data-points corresponding tothe high-energy modes are not error bars but the FWHM asobtained from the fit.19

It is worth mentioning that the Q resolution is very high,permitting us to identify that the broadening is associated tothe modes at =0.750±0.009. Therefore, the effect due to asteep dispersion integrated over a finite Q range, should bereduced in our case, if compared to inelastic neutron scatter-ing data.7,9,11 The fact that the width does not change notablyimplies that we are measuring mainly the intrinsicbroadening,11,12 originating from a damping process, and notan apparent one due to steep dispersion effect,20 as in Ref. 7.

The intensity of the two high energy modes is expected to

1 0.75 0.5 0.25 0ξ

0

2

4

6

8

10

12

14

16

18

20

ν(T

Hz)

3 3.25 3.5 3.75 4

∆1∆3

IXS FWHM

LA

1LO

2LO

3LO

4LO

5LO

6LO

Q = (4 - ξ, 0, 0)

0 0.25 0.5 0.75 1ν

0

10

20

30

40

50

60

70

80

90

hν(m

eV)

Q = (3, 1-ν, 0)

3.0 3.2 3.4 3.6 3.8 4.0( Qx , 0 , 0 )

0.00

0.10

0.20 LA

0.00

0.10

0.201LO

0.00

0.10

0.202LO

0.00

0.10

0.20

IXS

cros

sse

ctio

n(a

rb.u

n.)

x10 3LO

0.00

0.505LO

x100

0.00

0.50X100 6LO

Intensities T = 10 K(a)

(b)

FIG. 2. Left: dispersion of the phonon modes with polarizationvector e 1,0 ,0. Dispersion along the 1− 0,0 line has 1 lon-gitudinal symmetry and along the 0,1− 0 line has 3 transversesymmetry. Calculations lines are compared to the experimentalresults, as extracted from IXS spectra fit circles. Gray and dashedfilled correspond to two different experimental runs. Dashed barswith risers correspond to the fitted FWHM. Top x scale for 1

symmetry corresponds to Q= 4− ,0 ,0. Right: calculated IXScross section lines compared to the intensities extracted from IXSspectra fit for the longitudinal acoustic LA, and all optic modesbut the 4th one, which is extinguished in this Brillouin zone. Allfitted intensities are corrected by the Bose factor.


172507-3

be about the same at =0.25 but we find that it is reduced forthe 5LO mode compared to the 6LO, as shown in the rightpanel of Fig. 2. This may suggest a possible hybridization ofthe two modes in this q region. However, we should recallthat the calculation of intensity is less reliable than that offrequency, especially for simple models like the empiricatomic potential used here.

In conclusion, we report very high resolution inelasticx-ray scattering measurements of the phonon dispersion andlifetime in underdoped La2−xSrxCuO4+ for x=0.08. Wefound results that are in agreement with the previousreports12 at lower energy resolution. This suggests that theintrinsic broadening of the Cu-O bond stretching mode is

dominating at q= 0.25,0 ,0. The result appear incompatiblewith the interpretation of the broadening being due to a sharpdip in the dispersion but seems more likely due to the intrin-sic lifetime of the mode.

We acknowledge D. Gambetti and J. Nelayah for techni-cal help. This work was supported by ESRF through experi-ment HS-2440 and HS-2689 and by the U.S. Department ofEnergy under Contract No. DE-AC03-76SF00098. We ac-knowledge the support of the National Science Foundationthrough Grant No. DMR-0349361 and DMR-0405682. Weacknowledge the support from University of California, Ber-keley, through a France Berkeley Fund Grant.

*[email protected]†Institut de Minéralogie et de Physique des Milieux Condensés

IMPMC, CNRS UMR 7590, Campus Bouciaut, 140 rue deLourmel, 75015 Paris, France.

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15 M. d’Astuto, M. Calandra, S. Reich, A. Shukla, M. Lazzeri, F.Mauri, J. Karpinski, N. D. Zhigadlo, A. Bossak, and M. Krisch,Phys. Rev. B 75, 174508 2007.

16 R. Verbeni, F. Sette, M. H. Krisch, U. Bergmann, B. Gorges, C.Halcoussis, K. Martel, C. Masciovecchio, J. F. Ribois, G.Ruocco, and H. Sinn, J. Synchrotron Radiat. 3, 62 1996.

17 A. Mirone, OPENPHONON code source, 2001, available at http://www.esrf.fr/computing/scientific/

18 S. L. Chaplot, W. Reichardt, L. Pintschovius, and N. Pyka, Phys.Rev. B 52, 7230 1995.

19 Fitted FWHM on the energy scans corresponds to phonon line-width convoluted with instrumental resolution

20 Note that the apparent broadening due to dispersion depends onthe Q resolution and the stiffness of the dispersion, and it isdifferent both from intrinsic broadening of the phonon due to itsfinite lifetime, and instrumental energy resolution


172507-4

56 The bond stretching phonon dispersion

Chapter 6

The spectral waterfalls

Since the very rst ARPES data showing a band crossing Fermi surface(FS) were published for Bi2Sr2CaCu2O8+δ (Bi2212) [82], it is well knownthat the band structure near the Fermi energy (EF ) below 0.3 eV cannot bedescribed within the one electron band theory. The core discrepancy is thatthe experimental bandwidth is by a factor of 2 smaller than the prediction ofband structure calculation in the local density approximation (LDA). Thisdiscrepancy has been taken into account by considering a renormalization ofthe entire bandwidth due to the dressing of the hole by an antiferromagneticbackground[83]. Also, this high energy renormalization, from ≈ 1 eV to ≈ 0.3eV, is a common feature of many theories starting from one-band or multi-band Hubbard Hamiltonians, but so far there has been no data to test thesetheories from this fundamental point of view.

The isotope work clearly highlighted the importance of a better under-standing of the incoherent hump seen in ARPES at binding energy higherthan the kink energy. However, the observation of a considerable self-energyeect on the energy-momentum dispersion at high energy is by itself a quietsurprising result for the following reason. ARPES photo-intensity I(k, ω) isa direct measure of the spectral function A(k, ω):

I(k, ω) ∝ MA(k, ω)f(ω)

where M is a matrix element and f(ω) is the Fermi function. The spectralfunction can in turn be related to the electron self-energy Σ(ω):

A(k, ω) =−1

π

Im(Σ(ω))

(ω − ε(k)−Re(Σ(ω)))2 + Im(Σ(ω))2

Where ε(k) is the non-interacting (bare) electron dispersion. This relationis extremely important since we can extract Re(Σ(ω)) and thus the energy

58 The spectral waterfalls

of the collective mode(s) the electrons interact with from ARPES. However,one of the caveats is that one need to know a priori ε(k). Various wayof extracting ε(k) from the incoherent hump are commonly used (e.g. [37,44]), and some rely on the hypothesis that Re(Σ(ω)) → 0 in the incoherenthump. This is equivalent of saying that in the incoherent hump, the electronscan shake o their dressing and disperse for a very short time like non-interacting electrons. The large isotope eect (30meV) observed at highbinding energy (≈ 200 meV) questions the validity of this hypothesis.

In rst publication (physica C), we report the discovery of two universalenergy scales, E1= 0.35-0.45eV and E2 =0.8-0.9eV, in the spectral functionof p-type cuprates superconductors, identied as the high energy anomaly.E1, is marked by a steep downturn of the main dispersion toward higherenergies, like a waterfall of spectral intensity. E2 is marked by the reap-pearance of a band-like excitation, dispersing toward Γ. The universalty ofthis anomaly is demonstrated with data on single layer Bi2Sr1.6La0.4Cu2O6+x

(Bi2201), double layer Bi2Sr2CaCu2O8+x (Bi2212), Pb-doped Bi2212 and op-timally doped La1.64Eu0.2Sr0.16CuO4 (Eu-LSCO). This behavior is found inthe normal and the superconducting states, and persists over a wide dopingrange, from undoped insulator to highly overdoped metal.

In the second publication (physical review letter) we report a new de-velopment on the exact properties of the anomaly, providing unique insighton the process of how a doped oxygen hole is progressively dressed into aquasiparticle in cuprates superconductors. We reported the rst evidence oftwo distinct dispersions at high energy and the striking reminiscence of thespinon and holon branches reported in a one dimensional system by Kim etal. [84]. However, the existence of such a phenomenon in a 2D system likethe cuprates is very controversial.

Universal waterfall-like feature in the spectral functionof high temperature superconductors

J. Graf a, G.-H. Gweon b,1, A. Lanzara a,b,*

a Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USAb Department of Physics, University of California, Berkeley, CA 94720, USA

Available online 19 March 2007

Abstract

By performing high resolution angle resolved photoemission spectroscopy (ARPES) experiments on four different families of p-typecuprates, over an energy range much bigger than investigated before, we report the discovery of a universal high energy anomaly in thespectral function. This anomaly is characterized by the presence of two new high energy scales E1 = 0.35–0.45 eV and E2 = 0.8–0.9 eVand the pinning of the main ARPES spectral function along the boundary of a diamond in the momentum space. This anomaly unveils amissing link between the doped oxygen holes and the quasiparticles, providing a full range of relevant interactions to the high Tc

problem.Published by Elsevier B.V.

PACS: 74.72.h; 74.25.Jb; 79.60.i

Keywords: Cuprates; ARPES; Strongly correlated electron systems; High temperature superconductors

Uncovering the key interactions, and hence the relevantenergy scales that give rise to the dressing of a doped oxy-gen hole at high energy into a quasiparticle, is one of themain unsolved issues in the high temperature superconduc-tivity field. In the case of conventional superconductors forexample, the identification of the phonon energy scale wasa keystone in the understanding of the superconductingmechanism [1,2]. For high temperature superconductors(HTSCs), although an equivalent low energy scale at0.04–0.08 eV has been already identified (‘‘kink’’) [3–9],whether other important interactions contribute to thequasiparticle formation process still remains an open ques-tion. Indeed, the fact that the ARPES kink of p-type cup-rates is difficult to understand due to its unusual high

energy behavior [10,9], in contrast to the kink of other sim-pler materials [11,12], strongly motivates such a question.

In this paper we report the discovery of two universalenergy scales, E1 = 0.35–0.45 eV and E2 = 0.8–0.9 eV, inthe spectral function of p-type cuprates superconductors,identified as the ‘high energy anomaly’ [13,14]. E1 ismarked by a steep downturn of the main dispersion towardhigher energies, like a waterfall of spectral intensity. E2 ismarked by the reappearance of a band-like excitation, dis-persing toward C. We provide a simple physical picturebehind this anomaly, suggesting that this high energyanomaly bears information on the true nature of the build-ing block of low energy quasiparticles in cuprates super-conductors. The low energy quasiparticle dispersingbetween EF and E1 is widely believed to represents themotion of a Zhang Rice Singlet (ZRS) [15] in the antiferro-magnetic environment (e.g. ZRS coupled to a copper spin).We propose that at E1, the singlet decouples from the cop-per spin, decaying in a continuum of incoherent excita-tions, resulting in the observed waterfalls.

0921-4534/$ - see front matter Published by Elsevier B.V.

doi:10.1016/j.physc.2007.03.005

* Corresponding author. Address: Materials Sciences Division, Law-rence Berkeley National Laboratory, Berkeley, CA 94720, USA.

E-mail address: [email protected] (A. Lanzara).1 Present address: Department of Physics, University of California,

Santa Cruz, CA 95064, USA.

www.elsevier.com/locate/physc

Physica C 460–462 (2007) 194–197

This continuum of excitations represent the motion ofthe ZRS. At E2, the shake-off process is complete and onlythe doped oxygen hole remains, explaining the LDA-likedispersion predicted long ago [18].

High resolution angle resolved photoemission spectros-copy experiments (ARPES) were performed at beamlines7.0.1, 10.0.1 and 12.0.1 of the Advanced Light Source inBerkeley on single crystals of single layer Bi2Sr1.6La0.4Cu2-O6+x (Bi2201), double layer Bi2Sr2CaCu2O8+x (Bi2212),Pb-doped Bi2212 and optimally doped La1.64Eu0.2Sr0.16-CuO4 (Eu-LSCO) over an energy range much bigger thanpreviously investigated [16,17]. The doping of each samplewas cross-checked with the nominal value using the mea-sured superconducting-gap value and the binding energyof the Van Hove singularity. Data were taken at differentphoton energies, polarizations and temperature. The exper-imental conditions reported in this paper are summarizedin Table 1. The total energy and angular resolutions wereless than 50 meV and less than 0.07 A1, sufficient for thestructures studied here. Except for the Bi2201 data, mea-sured in the first Brillouin zone (BZ), all the data were mea-sured in both the first and the second BZs. In this paper‘low energy’ indicates the energy range between EF andE1 and ‘high energy’ the energy range between E1 and thevalence band complex at about 1 eV.

Fig. 1 shows the ARPES intensity vs energy andmomentum along the C to Y direction, nodal directionfor four different p-type cuprates. The background wassubtracted and the intensity was normalized to the maxi-mum intensity of the momentum distribution curves(MDC, momentum cuts at fixed energy) for each energystep. This MDC normalization scheme allows to easily fol-low the MDC peak position and width as a function ofenergy without any curve fitting. In addition to the lowenergy kink, not apparent within the energy-momentumwindow used in the figure, a surprising sudden downturnof the dispersion, toward a nearly vertical feature (see whitedotted line), occurs at 0.35 eV (see arrow). This identifiesa new energy scale, E1 = 0.35–0.45 eV, which is also char-acterized by a sudden decrease of the spectral intensity.From now on we will simply refer to this feature as the‘waterfall’. This waterfall extends from E1 to E2 and ischaracterized by a well defined and almost energy indepen-dent peak in the MDCs.

The waterfall discussed in Fig. 1 persists also in otherportion of the BZ, as shown in Fig. 2, where we reportthe MDC-normalized maps for the OD-Bi2212 from thenodal to the near antinodal region (cuts a0–a8) and forthe optimally doped Eu-LSCO at the antinodal point, b1.The MDC-normalization scheme reveals a waterfall-likefeature for each cuts. The waterfalls start from the bottomof the low energy dispersion or E1, whichever occurs firstalong the momentum cut. It is remarkable that the water-falls are so well localized in the momentum space over alarge energy window for each cut.

The LDA band (dotted gray line in panel a1) [18], plottedin the same figure for comparison, shows a good agreementwith the experimental data along the nodal direction at anenergy of 0.8–0.9 eV. This allows us to identify a newenergy scale E2 = 0.8–0.9 eV where the MDC peak startsdispersing again toward the C point. However, we note thatit is hard to follow the MDC dispersion all the way to the Cpoint due to the onset of another dispersing band of highspectral weight, associated with the valence band complexof Bi2212 [19], whose maximum is at 0.9 eV at the C point.

Table 1Summary of the samples characteristic (family, doping and criticaltemperature, Tc), and of the experimental conditions (photon energy(hm) and polarization of the light with respect to the sample (see Fig. 1))used for the data here presented

Sample Tc (K) hm (eV) Polarization

Bi2212 UD 64 52 Pb

Bi2212 OPT 91 52 Pb

Bi2212 OD 65 33 Pa

Bi2201 OPT 32 33 Pa

Eu-LSCO OPT 15 55 Pb

Pb-Bi2212 OD 65 60, 130 Pb

Fig. 1. MDC-normalized maps for four different families of cupratesuperconductors at 25 K: (a) OD Pb-Bi2212, (b) opt-doped Bi2212, (c)opt-doped Bi2201 and (d) opt-doped Eu-LSCO. Data are taken along thenodal direction, as shown in the inset of panel d. Black representsmaximum of intensity and white zero intensity. The light polarization wasalways along the C–X direction (Pa), but for some of the data (see Table1), the main component was out of plane (Pb).

Fig. 2. (a, b) MDC-maps for OD-Bi2212 and opt-doped Eu-LSCO. Themomentum position of the cuts a1–a8 and b1 are shown in the inset. TheLDA band is shown with a gray dotted line for comparison in panel a [18].

J. Graf et al. / Physica C 460–462 (2007) 194–197 195

In Fig. 3 we show the MDC dispersions (solid line),extracted by fitting the MDC curves with Lorentzian, forthe OD-Bi2212 (panel a) and Eu-LSCO (panel b) fromthe nodal to the antinodal direction. The location of eachcut is indicated in the inset of the same figure. In the caseof Bi2212 we also show the EDC dispersion, extracted fromthe position of the EDC peak maximum. An overall goodagreement is seen between OD-Bi2212 and Eu-LSCO.However, we observe two main differences. First, thewaterfalls in the nodal region of Eu-LSCO are not as steepas for Bi2212. Second, we could not distinguish a peak any-more in the MDCs of the LSCO data at E2. This couldhowever just be due to the lower sample surface quality.

We show in Fig. 4 the full momentum dependence of thewaterfalls. The ARPES intensity integrated between EF

and E2 for the four different families of cuprates reportedhere is shown. The data reveal the presence of a largemomentum region around C of very low spectral weight,consistent with the sudden decrease of intensity of theEDC peak observed at E1 [13,14]. Note that the spectralweight within this region is not zero, as shown by the inten-sity profile along (p, 0)–(0,0).

It is important to point out that the high energy anom-aly here discussed cannot be explained in terms of ARPESmatrix element, as it is a robust feature of the data indepen-dent of photon energy, polarization setting and BZ loca-tion. We note that a similar suppression of the ARPESspectral intensity near the C point has been reported inthe literature for another p-type cuprate [20].

A possible candidate for the novel behavior presented inthis paper is the coupling of electrons to high energybosons-like plasmons. While in plane plasmons can be avaluable candidate given their high energy [21], it is hardto explain the persistence of the high energy anomaly inthe undoped compound [22].

On the other hand, the material independence of thewaterfall and the presence of a similar anomaly in otherMott insulators [23], suggest that the two energy scalesE1 and E2 represent a complex interplay of the bare oxygenhole with the spin-lattice background. In addition, the dop-ing independence means that the high energy interactionsare at the scale of few lattice constants, since the antiferro-magnetic correlation length decreases to two lattice con-stants when the doping increases to optimal doping andbeyond [24].

As proposed by Graf et al. [14], we believe that the datasuggest that the low energy quasiparticle, between EF andE1 is a local composite fermion made of a charge +e ZhangRice singlet (ZRS) and a copper spin 1/2, bound together tomake a composite fermion with the right quantum numberto be observed by ARPES. This composite fermions is fur-ther dressed by the lattice through a strong electron–pho-non interaction, that affects the dispersion from EF to atleast E0 [9,25–31]. At E1, the composite fermion breaksdown and disintegrates into a ZRS and a copper spin. Inthe energy range from E1 to E2, the electronic excitationshave very little overlap with the photo-hole generated bythe photoemission process (as the ZRS does not have theright quantum number to be observed by ARPES). Theintensity stems from the tails of the EDCs of the closestband-like excitations. At energy E2 the ZRS finally disinte-

Fig. 3. MDC and EDCs dispersions for the OD-Bi2212 (upper panel) andopt-doped Eu-LSCO (lower panel) from nodal to antinodal direction. Thelocation of each cuts is indicated in the inset of the upper panel. Solid lineare dispersions extracted from the MDCs peak positions, while gray circlesare dispersions extracted from EDC peak positions (upper panel only).The two energy scale E1 and E2 are shown by arrows.

Fig. 4. Panels a–d show the ARPES intensity integrated from EF to 0.8 eVfor Pb-Bi2212 in the second BZ (panel a), OD-Bi2212 in the first BZ (panelb), opt-doped Bi2201 (panel c) and opt-doped Eu-LSCO in the second BZzone (panel d). An intensity profile along (p, 0)–(0,0) is shown in panelb, after subtraction of the elastic background. The antiferromagneticBrillouin zone (AF-BZ) is shown in the same figure for comparison(dotted line).

196 J. Graf et al. / Physica C 460–462 (2007) 194–197

grates into a bare oxygen hole and a copper spin, the first ofwhich explains the re-emergence of a band-like dispersion.

This result suggests the important role of the high energyphysics [32–35] to determine the true nature of the lowenergy excitations in the cuprates and together with otheruniversal properties in these materials [4,10,36,37] addanother important piece of evidence to the high Tc puzzle.

Acknowledgements

We thank D.H. Lee, A. Bill for useful discussions, and S.I.Uchida, H. Eisaki, H. Takagi and T. Sasagawa for providingus with high quality single crystals for this study. We alsothank A. Bostwick and A.V. Fedorov for experimental help.This work was supported by the National Science Founda-tion through Grant No. DMR03-49361 and the Director,Office of Science, Office of Basic Energy Sciences, Divisionof Materials Sciences and Engineering of the US Depart-ment of Energy under Contract No. DEAC03-76SF00098.

References

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tivity, vol. 1, M. Dekker Inc., New York, 1969, p. 561 (Chapter 11).[3] P.V. Bogdanov et al., Phys. Rev. Lett. 85 (2000) 2581.[4] A. Lanzara et al., Nature 412 (2001) 510.[5] P.D. Johnson et al., Phys. Rev. Lett. 87 (2001) 177007.[6] A. Kaminski et al., Phys. Rev. Lett. 86 (2001) 1070.

[7] A.D. Gromko et al., Phys. Rev. B 68 (2003) 174520.[8] T. Cuk et al., Phys. Rev. Lett. 93 (2004) 117003.[9] G.H. Gweon et al., Nature (2004).

[10] X.J. Zhou et al., Nature 423 (2003) 398.[11] M. Hengsberger et al., Phys. Rev. Lett. 83 (1999) 592.[12] T. Valla et al., Phys. Rev. Lett. 83 (1999) 2085.[13] J. Graf et al., Bull. A. P. S. 51 (2006) 1591.[14] J. Graf et al., Phys. Rev. Lett. 98 (2007) 067004.[15] F.C. Zhang, T.M. Rice, Phys. Rev. B 37 (1988) 3759.[16] A. Damascelli et al., Rev. Mod. Phys. 75 (2003) 473.[17] J.C. Campuzano et al., Physics of Superconductors, vol. II, Springer,

Berlin, 2004.[18] H. Lin et al., Phys. Rev. Lett. 96 (2006) 097001.[19] S. Sahrakorpi et al., private communication.[20] F. Ronning et al., Science 282 (1998) 2067.[21] B.S. Markievicz, A. Bansil, private communication.[22] F. Ronning et al., Phys. Rev. B. 71 (2005) 094518.[23] J. Denlinger et al., private communication.[24] M.A. Kastner et al., Rev. Mod. Phys. 70 (1998) 897.[25] K.A. Muller, Essential Heterogeneities in Hole-Doped Cuprate

Superconductors, vol. 114, Springer, 2005.[26] B.I. Kochelaev et al., Phys. Rev. Lett. 79 (1997) 4274.[27] A. Bianconi, M. Missori, Solid State Commun. 91 (1994) 287.[28] S.J.L. Billinge, T. Egami, Phys. Rev. B 47 (1993) 14386.[29] P. Calvani et al., Phys. Rev. B 53 (1996) 2756.[30] A.S. Mishchenko, N. Nagaosa, Phys. Rev. Lett. 93 (2004) 036402.[31] K.M. Shen et al., Phys. Rev. Lett. 93 (2004) 267002.[32] P. Phillips et al., Phys. Rev. Lett. 93 (2004) 267004.[33] V.J. Emery, G. Reiter, Phys. Rev. B 38 (1988) 4547.[34] C.L. Kane et al., Phys. Rev. B 39 (1989) 6880.[35] A. Macridin et al., Phys. Rev. B 71 (2005) 134527.[36] Z.A. Xu et al., Nature 406 (2000) 486.[37] P. Bourges et al., Science 288 (2000) 1234.

J. Graf et al. / Physica C 460–462 (2007) 194–197 197

Universal High Energy Anomaly in the Angle-Resolved Photoemission Spectra of HighTemperature Superconductors: Possible Evidence of Spinon and Holon Branches

J. Graf,1,2 G.-H. Gweon,3,4 K. McElroy,1 S. Y. Zhou,3 C. Jozwiak,3 E. Rotenberg,5 A. Bill,3 T. Sasagawa,6,7 H. Eisaki,8

S. Uchida,9 H. Takagi,6,7,10 D.-H. Lee,1,3 and A. Lanzara1,3,*1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

2Swiss Federal Institute of Technology Lausanne, CH-1015, Lausanne, Switzerland3Department of Physics, University of California Berkeley, Berkeley, California 94720, USA

4Department of Physics, University of California Santa Cruz, Santa Cruz, California 95064, USA5Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA6Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan

7CREST, Japan Science and Technology Agency, Saitama 332-0012, Japan8AIST, 1-1-1 Central 2, Umezono, Tsukuba, Ibaraki, 305-8568, Japan

9Department of Physics, University of Tokyo, Yayoi, 2-11-16 Bunkyoku, Tokyo 113-8656, Japan10RIKEN (The Institute of Physical and Chemical Research), Wako 351-0198, Japan

(Received 25 May 2006; published 7 February 2007)

A universal high energy anomaly in the single particle spectral function is reported in three differentfamilies of high temperature superconductors by using angle-resolved photoemission spectroscopy. As wefollow the dispersing peak of the spectral function from the Fermi energy to the valence band complex, wefind dispersion anomalies marked by two distinctive high energy scales, E1 0:38 eV and E2 0:8 eV.E1 marks the energy above which the dispersion splits into two branches. One is a continuation of the nearparabolic dispersion, albeit with reduced spectral weight, and reaches the bottom of the band at the pointat 0:5 eV. The other is given by a peak in the momentum space, nearly independent of energy betweenE1 and E2. Above E2, a bandlike dispersion reemerges. We conjecture that these two energies mark thedisintegration of the low-energy quasiparticles into a spinon and holon branch in the high Tc cuprates.

DOI: 10.1103/PhysRevLett.98.067004 PACS numbers: 74.72.h, 74.25.Jb, 79.60.i

Understanding how doped oxygen holes are transportedin the environment of antiferromagnetically coupled cop-per spin is one of the most fundamental problems in thefield of high temperature superconductivity. It was pro-posed early on that the doped holes in the oxygen 2porbitals form singlets with the spins of the neighboringcoppers [1]. The resulting charge-e and spin-0 object iscalled the Zhang-Rice singlet (ZRS). As the ZRS movesthrough the CuO2 plane, the copper spins get rearranged.As a result, the ZRS couples very strongly to the antiferro-magnetic environment. Remarkably, as a consequence ofsuch strong coupling, quasiparticles emerge at low ener-gies. This is evidenced by the sharp nodal quasiparticlepeaks seen in angle-resolved photoemission (ARPES) ofalmost all cuprate compounds [2,3]. In simple physicalterms a quasiparticle is a composite object made of aZRS and a S 1

2 copper spins. It is widely believed that,at sufficiently low temperatures, superconducting pairingoccurs between these quasiparticles giving rise to the hightemperature superconducting state. Thus a microscopicunderstanding of the pairing mechanism of high Tc super-conductors requires an in-depth understanding of how aZRS is dressed into a quasiparticle.

Here we present the first systematic study of the evolu-tion of the ARPES spectral function from the Fermi level(EF 0) to the valence band complex (at energy 1 eV[4]) for three families of high temperature superconduc-tors. Our results provide a surprising new experimental

understanding on the quasiparticle formation process dis-cussed above. Specifically, by covering a much broaderenergy range than typically studied [2,3], we have identi-fied anomalies in the ARPES spectra occurring at two uni-versal high energy scales, E1 0:38 eV and E2 0:8 eVfrom EF. We conjecture that these two energies mark thethreshold for the disintegration of the low-energy quasi-particles at two different binding levels.

ARPES data have been collected at the AdvancedLight Source, beam lines 7.0.1, 10.0.1, and 12.0.1 forthree different families of hole-doped cuprates: singlelayer Bi2Sr1:6La0:4Cu2O6 (Bi2201), double layerBi2Sr2CaCu2O8 (Bi2212), and Pb-doped Bi2212(Pb2212) and for several doping values. The data presentedhere were measured at least in both the first and the secondBrillouin zones (BZs) and along the two polarization paand pb as shown in Fig. 1. The double layer Bi2212 datawere collected at 52 eV for the underdoped (UD) (Tc 64 K) and optimally doped (OPT) (Tc 91 K) sample,and 33 and 65 eV for the overdoped (OD) (Tc 80 K)sample. The OD Pb2212 (Tc 65 K) sample was mea-sured at 55, 60, and 75 eV and the OPT Bi2201 (Tc 32 K) sample at 33 eV. Unless specified otherwise, all thedata reported were measured at 25 K.

Figure 1 shows the ARPES intensity map as a functionof energy and momentum in the (0, 0)-(, ) direction foran (a) UD, (b) OPT, and (c) OD Bi2212. In all panels twomain features are apparent: a high intensity feature at low

PRL 98, 067004 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending9 FEBRUARY 2007

0031-9007=07=98(6)=067004(4) 067004-1 © 2007 The American Physical Society

energy (widely studied in the literature [2,3]), and a weakerintensity feature at high energy. The high energy feature,‘‘waterfall’’-like feature, is the main focus of this Letter.Given the large energy span of Fig. 1, the ‘‘kink’’ at E0 0:06 eV (gray arrows pointing to the right) is a very subtlefeature. Aside from the kink, the low-energy dispersion canbe well fitted by a single tight binding band [dotted grayline in panel (a)] [2,5]. Surprisingly, as the low-energydispersion reaches E1 0:38 0:07 eV, at momentumaround =4; =4 1

a (gray arrows pointing to the left),the dispersion suddenly undergoes a steep downturn ac-companied by a substantial drop of the ARPES intensity.The overall feature of this anomaly is nearly independentof doping.

In Fig. 2 we present selected raw EDCs (energy distri-bution curves, energy cuts at constant momentum; panel(a)] and MDCs [momentum distribution curves, momen-tum cuts at constant energy; panel (b)] for the OD Bi2212.We show results for the OD sample, making a strong casethat pseudogap [6,7], disorder and inhomogeneity [8–10]can be ruled out as possible origin. However, similarbehaviors are observed for all doping values we studied.

Panels (a) and (b) show that the behaviors of MDC andEDC peak become completely different as E1 is reached,exposing the full view of the anomaly. The EDC peaksshown in panel (a) disperse in a simple manner and, as themomentum moves away from the Fermi momentum, thepeak gets broader and weaker losing rapidly its strength asit approaches E1. This is consistent with the sudden de-crease of the ARPES intensity observed at E1 in Fig. 1. Incontrast, the raw MDCs in panel (b) show a well-definedpeak over the full energy range. For energy & E1, the MDCpeak disperses in a consistent fashion with the EDC dis-

persion, and as it reaches E1 it suddenly becomes almostenergy independent all the way up to E2. As the energyincreases beyond E2, the MDC peak starts dispersingagain. It is surprising that a well-defined MDC peak canstill be identified within this large energy range. A furthertracking of the MDC dispersion, well above E2, is madedifficult due to the strong valence band complex dominat-ing the ARPES signal, as seen by the strong rise of theintensity on the right end side of panel (a). Interestingly,the MDC peak width stops increasing at E1 and shows asmall decrease [inset of panel (b)].

From now on, we will refer collectively to the anomaliesat E1 and E2 as ‘‘high energy anomaly.’’ In Fig. 2(c) wereport MDC dispersions for different materials, variousdoping values, and different temperatures. It is clear thatthe overall features of the high energy anomaly and theirenergy and momentum locations are a universal feature inall the materials studied, from heavily overdoped to un-doped compound, and do not show any substantial changegoing from the superconducting to the normal state.

FIG. 2 (color online). (a),(b) EDCs from kF (top curve) toward and MDCs for the OD Bi2212. The spectra are verticallyshifted for an easy view. The small peaks on the right and left ofthe main MDC peak are due to the superstructure (SS). At 1 eV, the valence band can also be distinguished. The insetshows the FWHM of the MDC peak as a function of energy.(c) MDC dispersion, horizontally shifted for an easy view, forseveral compounds and doping. The Ca2CuO2Cl2 dispersion[19] is shifted in energy by 0.45 eV to account for the energygap. The OD-Bi2212 data are shown both above, 100 K, andbelow Tc, 25 K. The prime and double prime stand for data takenin the first and second BZ, respectively. The dashed line is theLDA band dispersion [20].

FIG. 1 (color online). ARPES intensity maps of Bi2212samples for three different doping values. Data for the overdopedsample are in the normal state, 100 K. The location of the cut isshown in the BZ diagram on the right side, along with thedifferent ARPES geometries used here. The gray dotted line isthe dispersion obtained from a tight binding fit [5] up to energy0.3 eV.


067004-2

Interestingly, beyond E2 the MDC dispersion is in a rea-sonable agreement with the LDA prediction [panel (c)].This gives an estimate of the energy scale of the measuredband to be 1:3–1:4 eV.

In Fig. 3 the full momentum space information about thehigh energy anomaly is summarized. Panels (a)–(h) showthe momentum space distribution of the ARPES intensityat different energies from EF to 1.3 eV. Representative datafrom OD Pb-Bi2212 are shown. From EF to E1 [panels(a)–(c)] the ARPES contour and the tight binding fit (whitesolid line) are in very good agreement. This region corre-sponds to the low energy region, below E1, of Figs. 1 and 2.As the energy increases, the E1 anomaly is marked unam-biguously by the strong departure of the data from the tightbinding fit and, over a wide energy region from E1 to E2

[panels (d)–(f)], the main ARPES intensity is ‘‘pinned’’ atthe boundary of a diamond (dashed line) whose four cor-ners are located near (=2a, 0) and (0, =2a). Wecaution readers that despite the color scale the spectralweight within this diamond is not strictly zero (Fig. 2).When the energy increases beyond E2 [panels (g),(h)],the ARPES intensity starts moving again toward ,consistently with the resumed dispersion of the MDCpeak discussed in Fig. 2. This is a common feature of allthe materials reported here and of optimally dopedLa1:64Eu0:2Sr0:16CuO4 (Eu-LSCO) [11].

We have searched for, but did not find, a similar anomalyin more conventional materials such as GaAs (a simpleband insulator), K0:9Mo6O17, SmTe3 [12] and CeTe2 [13](quasi-two-dimensional metals with conventional chargedensity wave orders), and graphite (a quasi-two-dimensional semimetal) [14]. However, a similar high

energy anomaly is also seen in several ruthenate com-pounds [15] suggesting that it might be an intrinsic featureof Mott physics.

We note that this peculiar high energy behavior de-scribed in Figs. 1–3 cannot be explained by the well-known ARPES matrix element effect [16]. The matrixelement is strongly sensitive to the experimental settingsin contrast to the high energy anomaly, e.g., predicting [17]that the intensity near the point is enhanced in the secondBZ, while it does predict an intensity depression in the firstBZ. Instead, we find a similar high energy behavior inde-pendently of the BZ, the photon energy (25, 33, 43, 52, 55,59, 75, 90, 100, 130, and 150 eV), or the light polarizationsettings (along the Cu-O bonds, along the Cu-Cu bonds,and normal to the CuO2 planes).

One possible explanation of the observed high energyanomaly is in terms of coupling to a bosonic mode along asimilar line as the low-energy kink. However, we believethis picture is unlikely since so far there is no known modeoccurring at these energies and robust over the wholedoping range, from zero doping to high overdoping.

A far more general possibility is that the data presentedhere show the disintegration of the low-energy quasi-particle. In this view, we propose that the dispersive bandin the energy range from E0 to E1 is the signature of acomposite object, as schematically represented in Fig. 3(j),made of a ZRS bound to a Cu spin 1

2 . This compositeparticle has quantum number S 1

2 and charge e and isconsistent with that of a photohole. At lower energies thiscomposite object is further dressed by phonons and low-energy collective spin excitations to become the ultimatequasiparticle in the energy range between EF and E0. The

FIG. 3 (color online). (a)–(h) Maps of the ARPES intensity in the momentum space at increasing energies for the Pb-Bi2212 sample.Data were taken in the second BZ and symmetrized according to the tetragonal symmetry. The color scale is normalized independentlyfor each cut. The white solid lines correspond to the tight binding fit and the dashed line diamond indicates the characteristic geometryof the high energy anomaly. (i) Three dimensional plot of the ARPES intensity as a function of energy and in-plane momentum. (j) Ourproposed scenario for the high energy anomaly.


067004-3

characteristics of the fermionic composite particle existingbetween E0 and E1 is the broad EDC and MDC peaks andtheir mutually consistent dispersions. At E1 this compositeobject breaks down into a ZRS and a copper spin. Theformer is referred as a ‘‘holon’’ and the latter a ‘‘spinon’’ inthe theory literature of high Tc. Experimentally this is seenas the sudden loss of spectral intensity of the broad dis-persive ARPES peaks at E1. In the energy range betweenE1 and E2 the photoemission spectrum is the convolutionof those of a spinon and a holon. In principle, the spectralfeatures associated with both excitations can be observedby ARPES [18,21].

By tuning the energy (60 eV) and the polarization (out-of-plane) of the photon, we have observed for the first timea new dispersive feature [dotted line in Fig. 4(a)] whosebottom occurs at 0:5 eV at the point. The correspond-ing peak of this new branch can be observed both in theMDCs and also in the EDCs spectra [panels (c),(d)]. Weinterpret this new feature as the spinon branch while thewaterfall feature as the holon branch. The two peaks in theMDCs [panel (c)] in the energy range above 0.4 eV andbelow 0:5 eV represent the two branches. This interpre-tation is supported by the striking similarity between ourdata [panel (a)] and the recent photoemission result ofthe spinon and holon branches of the one dimensionalcuprate ([panel (b)] [18]. Note, however, that, while thecomparison between panels (a),(b) is quite appealing, notonly qualitatively but also quantitatively, in our case twopeaks can be observed only in MDCs but not in EDCs, dueto the puzzling near-vertical nature of the holon dominatedbranch (waterfall). Finally, E2 is the energy where the ZRSdisintegrates into a bare oxygen hole and a copper spin.This reappearance of the fermionic oxygen hole explainsthe reemergence of a bandlike dispersion. Obviously, more

investigations would be necessary to test our conjecturefurther.

In conclusion, we have reported for the first time auniversal high energy anomaly in the ARPES spectra ofdifferent families of high temperature superconductors,identified by a sudden change in the dispersion of themain spectral peak. This phenomenon is robust under thechange of doping, as well as chemical composition. Weconjecture that the high energy anomaly provides the long-sought-after evidence of spin charge separation in the highTc compounds.

We would like to thank P. W. Anderson, A. Bansil,A. Bianconi, C. Di Castro, C. Castellani, S. Chakraverty,J. E. Hirsch, T. Egami, M. Jarrell, S. Kivelson, R. S.Markiewicz, A. Macridin, V. Oganesyan, P. Phillips,A. Perali, and S. Sahrakorpi for useful discussions andA. Bostwick and A. V. Fedorov for experimental help.This work was supported by the Director, Office ofScience, Office of Basic Energy Sciences, Division ofMaterials Sciences and Engineering, of the U.S.Department of Energy under Contract No. DE-AC03-76SF00098, and by the National Science Foundationthrough Grant No. DMR-0349361. ALS is operated bythe DOEs Office of BES, Division of Materials Science,under Contract No. DE-AC03-76SF00098.

*Electronic address: [email protected][1] F. C. Zhang and T. M. Rice, Phys. Rev. B 37, 3759 (1988).[2] A. Damascelli, Z. Hussain, and Z.-X. Shen, Rev. Mod.

Phys. 75, 473 (2003).[3] J. C. Campuzano, M. R. Norman, and M. Randeria,

Physics of Superconductors (Springer, New York, 2004),Vol. II.

[4] B. O. Wells et al., Phys. Rev. B 40, 5259 (1989).[5] G.-H. Gweon et al., Nature (London) 430, 187 (2004).[6] A. G. Loeser et al., Science 273, 325 (1996).[7] H. Ding et al., Nature (London) 382, 51 (1996).[8] S. H. Pan et al., Nature (London) 413, 282 (2001).[9] T. R. Thurston et al., Phys. Rev. B 40, 4585 (1989).

[10] P. A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod. Phys.78, 17 (2006).

[11] J. Graf et al. (unpublished).[12] G.-H. Gweon et al., Phys. Rev. Lett. 81, 886 (1998).[13] D. Garcia (private communication).[14] S. Y. Zhou et al., Phys. Rev. B 71, 161403(R) (2005).[15] J. Denlinger (private communication).[16] A. Bansil and M. Lindroos, Phys. Rev. Lett. 83, 5154

(1999).[17] A. Bansil (private communication).[18] B. J. Kim et al., Nature Phys. 2, 397 (2006).[19] F. Ronning et al., Phys. Rev. B 71, 094518 (2005).[20] H. Lin, S. Sahrakorpi, R. S. Markiewicz, and A. Bansil,

Phys. Rev. Lett. 96, 097001 (2006).[21] A. Bianconi et al., Physica (Amsterdam) 317C, 304

(1999).

FIG. 4 (color online). Second derivatives of ARPES intensitymaps along the nodal direction of Pb2212 (a) and SrCuO2

(b) [18]. Only negative values of second derivatives are shown,to trace peaks but not dips. Sum of the second momentum-derivative and the second energy-derivative is shown at eachpoint. (c),(d) MDCs and EDCs from the data shown in panel (a).The MDCs and EDCs are vertically shifted for an easy view. Thedotted line and the dashed line highlight the proposed spinon andholon dispersions, respectively.


067004-4

Chapter 7

Conclusions

In this thesis I presented new results and insights on the many layers of dress-ing that inuence the superconducting charge carriers in the cuprate hightemperature superconductors. All the results point out that the spin, lattice,electronic and Fermi surface topology play a complex role through mutualinteractions that can not be neglected in any realistic theory of high tem-perature superconductivity. This has been possible by combining ARPES,isotope substituted ARPES and IXS study.

In particular, we report at low energy: 1) First experimental results show-ing the eect of an isotope substitution on the electronic structure of cuprates.In particular I showed that the kink energy is isotope dependent and thatthe eect of the isotope substitution gets stronger near the BZ face, wherethe gap is stronger. 2) First experimental evidence of an anomaly in thedispersion of the Cu-O bond stretching, half breathing phonon, for singlelayer Bi2Sr2−xCu2O6+δ, similar to the one observed in other cuprates fam-ilies. With an additional IXS study on La2−xSrxCu2O4, I showed that theanomalous broadening accompanying the softening is due to intrinsic damp-ing rather than to a steep dispersion. 3) The rst report of a low energykink (35meV) in the antinodal region of the electronic spectra of single layerBi2Sr2−xCu2O6+δ, coexisting with the higher kink at 60 meV previously re-ported. 4) Uncover the full momentum location of the two kink in the disper-sion. In particular we observed that the 60 meV kink exist only around in theregion where the Fermi arcs are dened. As the Fermi arc tip is reached, allthe way to the BZ face, the 35 meV becomes dominant. 5) By direct compar-ison with the phonon dispersion, both in terms of energy and momentum, weshow that the soft part of the Cu-O bond stretching, half breathing phononis the one that strongly couples to the quasiparticles giving rise to the 60meV kink along the Fermi arc.

By extending these studies to higher energy, all the way to the valence

band complex we report: 1) First evidences for an universal anomaly in theARPES high binding energy spectra of the cuprates. Our data revealed thatthe dispersion near the Γ point, hitherto believed to approach ∼500 meV atthe Γ point, actually branches o into a very steep band at about 0.5 π/aaway from the Γ point that dives into the oxygen band complex starting at 1eV binding energy, and then slowing down rapidly to reach a band minimumof ∼1.5 eV at the Γ point. I dubbed this high energy kink the waterfallto enhance the fact that in this case, the kink in the dispersion is likely notdue the coupling to sharp bosonic mode. We conjecture that the high energyanomaly provides the long sought-after evidence of spin charge separation inthe high Tc compounds. Though a full understanding of this anomaly is notyet within reach, this work clearly stimulated a new approach and a freshview on the problem as testied by the numerous publications that followed[85, 10, 11, 86, 87, 88, 89, 90].

Finally, on the experimental side, I presented my contribution in buildinga state of the art laser based ARPES system from ground up and the rstresults. In addition, I presented our on-going spin resolved time of ightARPES system and our future perspective in term of time-spin-angle resolvedphotoemission.

The race for room temperature is still on, but I hope to have added a fewpieces to the high temperature superconductors puzzle and motivated newapproaches to this long standing mystery.

List of Abbreviations

ARPES . . . . . . . . . . angle resolved photoemission electron spectroscopyBi2201 . . . . . . . . . . . Bi2Sr2−xCu2O6+δ

Bi2212 . . . . . . . . . . . Bi2Sr2CaCu2O8+δ

BS . . . . . . . . . . . . . . . bond stretchingBZ . . . . . . . . . . . . . . . Brillouin zoneEDC . . . . . . . . . . . . . energy distribution curveESRF . . . . . . . . . . . . European Synchrotron Radiation FacilityFS . . . . . . . . . . . . . . . Fermi surfaceFWHM . . . . . . . . . . full width half maximumHTSC . . . . . . . . . . . high temperature superconductorINS . . . . . . . . . . . . . . inelastic neutron scatteringIXS . . . . . . . . . . . . . . inelastic X-ray scatteringLDA . . . . . . . . . . . . . local density approximationLO . . . . . . . . . . . . . . longitudinal opticalMDC . . . . . . . . . . . . momentum distribution curveOD . . . . . . . . . . . . . . over-dopedOPT . . . . . . . . . . . . . optimally-dopedUD . . . . . . . . . . . . . . under-dopedZRS . . . . . . . . . . . . . Zhang-Rice singlet

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Curriculum Vitae

Experiences

Oct 02- Lawrence Berkeley National Laboratory (LBNL)present Advanced Light Source and Material Science Division

Prof. Alessandra Lanzara- Spin-polarized low energy electron microscopy of ferromagneticthin-lms- Laser and synchrotron based angle resolved photoemission(ARPES) and inelastic x-rays scattering (IXS) with strongly cor-related materials- Referee for Physical Review Letters

Aug & Swiss Light Source (PSI)Sep 01 Material Science Beamline

Dr. Bruce D. Patterson & Dr. H.-J. Weyer- Pilot experiment for a full phase and time resolved synchrotronhard x-r ay diraction analysis of Portland Cement with modiedcellulose ethers

Oct 99- Institute of photonic and quantum electronics (EPFL)

Oct 00 Laboratory of Quantum OptoelectronicsProf. B. Deveaud-Pledran- Development and setup of a modular photoluminescence excita-tion set-up (software and hardware).

http://www.lbl.gov

http://prl.aps.org

http://www.psi.ch

http://imowww.epfl.ch/

Education

2004- PhD Thesispresent Swiss Federal Institute of Technology

School of Basic Sciences, Section of Physics &Prof. G. MargaritondoLawrence Berkeley National Laboratory (LBNL)Advanced Light Source and Material Science DivisionProf. A. Lanzara

1997- Diploma (Master degree)

2003 Swiss Federal Institute of TechnologySchool of Basic Sciences, Section of Physics

http://www.lbl.gov

Published work

2007 12. Bond stretching phonon softening and ARPES kinkin Bi2Sr1.6La0.4Cu2O6+δ

J. Graf, M. d'Astuto, D. Garcia, N.-L. Saini, M. Krisch, A.Q.RBaron, H. Eisaki, and A. LanzaraPhys. Rev. Lett., In press.

11. In-plane copper-oxygen bond-stretching modeanomaly in underdoped La2−xSrxCuO4+δ measured withhigh-resolution inelastic x-ray scatteringJ. Graf, M. d'Astuto,P. Giura, N.-L. Saini, A. Bossak, M. Krisch,S.-W. Cheong, A. Shukla,S. Takao, and A. LanzaraPhys. Rev. B 76, 172507 (2007)

10. Universal waterfall-like feature in the spectral func-tion of high temperature superconductorsJ. Graf, G.-H. Gweon, and A. LanzaraPhysica C 460, 194 (2007)

9. Universal High Energy Anomaly in the Angle-Resolved Photoemission Spectra of High TemperatureSuperconductors: Possible Evidence of Spinon and HolonBranchesJ. Graf, G.-H. Gweon, K. McElroy, S. Y. Zhou, C. Jozwiak, E.Rotenberg, A. Bill, T. Sasagawa, H. Eisaki, S. Uchida, H. Takagi,D.-H. Lee, and A. Lanzara(Selected by John R. Clem for publicaction in Virtual Journalof Applications of Superconductivity)Phys. Rev. Lett. 98, 067004 (2007)

8. Revealing Charge Density Wave Formation in theLaTe2 System by Angle Resolved Photoemission Spec-troscopyD. R. Garcia, G.-H. Gweon, S. Y. Zhou, J. Graf, C. M. Jozwiak,M. H. Jung, Y. S. Kwon, and A. LanzaraPhys. Rev. Lett. 98, 166403 (2007)

http://link.aps.org/abstract/PRB/v76/e172507



http://dx.doi.org/10.1016/j.physc.2007.03.005


http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000098000006067004000001&idtype=cvips&gifs=yes




http://scitation.aip.org/dbt/dbt.jsp?KEY=VIRT03&Volume=12&Issue=4

http://scitation.aip.org/dbt/dbt.jsp?KEY=VIRT03&Volume=12&Issue=4




2006 7. First direct observation of Dirac fermions in graphiteS. Y. Zhou, G.-H. Gweon, J. Graf, A. V. Fedorov, C. D. Spataru,R. D. Diehl, Y. Kopelevich, D.-H. Lee, Steven G. Louie, A. Lan-zaraNature Physics 2, 595 (2006)

6. Interface Coupling Transition in a Thin Epitaxial An-tiferromagnetic Film Interacting with a FerromagneticSubstrateM. Finazzi, A. Brambilla, P. Biagioni, J. Graf, G.-H. Gweon, A.Scholl, A. Lanzara, and L. DuòPhys. Rev. Lett. 97, 097202 (2006)

5. Elastic scattering susceptibility of the high temper-ature Bi2Sr2CaCu2O8+δ superconductor: A comparisonbetween real and momentum space photoemission spec-troscopiesK. McElroy, G.-H. Gweon, J. Graf, S. Uchida, H. Eisaki, H. Tak-agi, T. Sasagawa, D.-H. Lee, and A. LanzaraPhys. Rev. Lett. 96, 067005 (2006)

2005 4. Mapping the spin-dependent electron reectivity of Feand Co ferromagnetic thin lmsJ. Graf, C. Jozwiak, A. K. Schmid, Z. Hussain, and A. Lanzara(Selected by David Awschalom for publicaction in Virtual Jour-nal of Nanoscale Science & Technology)Phys. Rev. B 71, 144429 (2005)

3. Coexistence of sharp quasiparticle dispersions and dis-order features in graphiteS. Y. Zhou, G.-H. Gweon, C. D. Spataru, J. Graf, D.-H. Lee,Steven G. Louie, and A. LanzaraPhys. Rev. B 71, 161403(R) (2005)

2. Oxygen isotope eect on electron dynamics inBi2Sr2CaCu2Oy: angle-resolved photoemission spec-troscopyT. Sasagawa, A. Lanzara, G.-H. Gweon, S. Zhou, J. Graf, Suryadi-jaya and H. TakagiPhysica C 426, 436 (2005)

http://www.nature.com/nphys/journal/v2/n9/abs/nphys393.html

http://link.aps.org/doi/10.1103/PhysRevLett.97.097202









http://www.vjnano.org

http://www.vjnano.org






2004 1. An unusual isotope eect in a high-transition-temperature superconductorG.-H. Gweon, T. Sasagawa, S.Y. Zhou, J. Graf, H. Takagi, D.-H.Lee, A. LanzaraNature 430, 187 - 190 (2004)

Conferences

2007 APS March meeting (Denver, USA)Inelastic X-ray scattering study of the bond stretching phononmode in Bi2Sr2xCu2O6+δ (contributed talk)Universal spectral weight transfer in high temperature supercon-ductors (contributed talk)

ALS photoemission workshop (Berkeley, USA)Spectral Waterfalls in the Cuprates (invited talk)

2006 APS March meeting (Baltimore, USA)Spectral Waterfalls in the Cuprates (contributed talk)

2005 Mottness and Quantum Criticality Workshop (Tobago,West Indies)Elastic scattering susceptibility of high temperature superconduc-tors: A comparison between a real and a momentum space spec-troscopy (poster)

2004 APS March Meeting (Montreal, Canada)Mapping the quantum well eects in Fe and Co ferromagneticthin lms (contributed talk)

http://www.nature.com/nature/journal/v430/n6996/abs/nature02731.html

http://www.nature.com/nature/journal/v430/n6996/abs/nature02731.html

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Kinks in the angle resolved photoemission and inelastic x...

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