Momentum dependent dxz/yz band splitting in LaFeAsO

S. S. Huh,1, 2 Y. S. Kim,1, 2 W. S. Kyung,1, 2 J. K. Jung,1, 2 R. Kappenberger,3 S.

Aswartham,3 B. Buchner,3, 4 J. M. Ok,5, 6 J. S. Kim,5, 6 C. Dong,7, 8 J. P. Hu,7, 8

S. H. Cho,9 D. W. Shen,9 J. D. Denlinger,10 Y. K. Kim,11, 12 and C. Kim1, 2, ∗

1Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Republic of Korea2Department of Physics and Astronomy, Seoul National University (SNU), Seoul 08826, Republic of Korea

3Leibniz Institute for Solid State and Materials Research, IFW-Dresden, 01069 Dresden, Germany4Institute of Solid State Physics, TU Dresden, 01069 Dresden, Germany

5Center for Artificial Low Dimensional Electronic Systems,Institute of Basic Science, Pohang 790-784, Korea

6Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea7Beijing National Laboratory for Condensed Matter Physics,

and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China8Collaborative Innovation Center of Quantum Matter, Beijing, China

9State Key Laboratory of Functional Materials for Informatics,Shanghai Institute of Microsystem and Information Technology (SIMIT),

Chinese Academy of Sciences, Shanghai 200050, People’s Republic of China10Advanced Light Source, Lawrence Berkeley National Laboratory, California 94720, USA

11Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea12Graduate school of Nanoscience and Technology,

Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea(Dated: March 25, 2020)

We performed angle-resolved photoemission spectroscopy (ARPES) studies of the electronic struc-ture of the nematic phase in LaFeAsO. Degeneracy breaking between the dxz and dyz hole bandsnear the Γ and M point is observed in the nematic phase. Different temperature dependent bandsplitting behaviors are observed at the Γ and M points. The energy of the band splitting near theM point decreases as the temperature decreases while it has little temperature dependence nearthe Γ point. The nematic nature of the band shift near the M point is confirmed through a detwinexperiment using a piezo device. Since a momentum dependent splitting behavior has been observedin other iron based superconductors, our observation confirms that the behavior is a universal oneamong iron based superconductors.

PACS numbers:

I. INTRODUCTION

The discovery of iron based superconductors (IBS) overa decade ago brought renewed interest in high TC su-perconductivity research [1, 2]. In addition to the su-perconductivity itself, its various phases have attractedmuch attention due to their possible relation to super-conductivity. Among these phases, the nematic phase, arotational symmetry broken state in the electronic struc-ture, has been intensively studied as it also occurs inother unconventional superconductors [3]. Moreover, thedivergent nematic susceptibility at the optimal dopingsuggests that the nematic fluctuation may play an im-portant role in the formation of the Cooper pairs in IBS[4, 5]. Therefore, understanding the origin of the nematicphase can be a key to unraveling the mechanism of theunconventional superconductivity in IBS.

A number of angle-resolve photoemission spectroscopy(ARPES) experiments have been conducted to investi-gate the rotational symmetry broken electronic states.However, interpretations of experimental data differ fromeach other, making the origin of the nematic phase a morecontroversial issue. Various scenarios were proposed as

the origin of the nematic phase based on ARPES results,such as simple Ferro-orbital order [6, 7], d-wave bond or-der [8], unidirectional nematic bond order [9], and signreversal order [10]. Among various candidates, the insta-bility of the momentum dependent band splitting whichis commonly observed in FeSe, NaFeAs and BaFe2As2 isfavored as the true origin of the nematic phase [11–13].

In resolving such issue, confirming if the behavior ofthe nematic electronic structure is universal among IBSshould be an important step. Despite the intensive re-search on the nematic phase, there is a lack of APRESstudy on the nematic phase of LaFeAsO even though it isthe first IBS that was discovered [14, 15]. Therefore, in-vestigating electronic structure of the LaFeAsO nematicphase is an important step towards finding the origin ofthe nematic phase. In this work, we performed tempera-ture dependent ARPES experiments on twinned and de-twinned LaFeAsO crystals. The results show a nematicbehavior similar to other IBS: finite near the M pointbut very small near the Γ point [11–13]. Our observa-tion of the momentum dependent nematic band splittingestablishes a universal nematic behavior in IBS.

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II. EXPERIMENT

High quality LaFeAsO single crystals were synthesizedby using solid state crystal growth technique [16]. Thestructural and magnetic transition temperatures (TS andTN ) were found to be around 145 and 127 K, respec-tively [16, 17]. ARPES measurements were performed atthe beam line 4.0.3 of the Advanced Light source (ALS)and beam line 03U of the Shanghai Synchrotron Radia-tion Facility (SSRF), and also with a lab-based system atSeoul National University (SNU). Piezo detwin ARPESexperiments were performed with the system at SNU.150 V bias voltage was applied to the piezo device to de-twin samples. All spectra were acquired with VG-Scientaelectron analyzers. The samples were cleaved in an ul-trahigh vacuum better than 5× 10−11 torr. To minimizethe aging effect, all the data were taken within 8 hoursafter cleave.

III. RESULTS AND DISCUSSION

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FIG. 1: (Color online). (a) Fermi surface map taken with80 eV and p-polarized light. The inset shows the intensitynear the M point multiplied by 10 to show the details. (b)Corresponding band structure at the Γ and M points alongthe Γ-M direction. The red and blue dashed line indicatedispersions of dxz/yz and dxy bands, respectively. (c) and (d)Similar measurements but with s-polarized light. All the datawere taken at 30 K.

Figs. 1(a) and 1(c) show Fermi surface maps ofLaFeAsO taken with p- and s-polarized 80 eV light, re-spectively. Considering all the features of the two Fermisurface maps taken with different polarizations, we de-termine that the Fermi surface consists of three circularpockets around the Γ point and two peanut like pock-ets around the M point. Due to the low intensity near

the M point, the intensity of the Fermi surface nearthe M point is multiplied by 10 and depicted in the in-set. The observed Fermi surface topology is consistentwith that from previous ARPES studies on LaFeAsO[14, 15, 18, 19]. Band structures near Γ and M are shownin Figs. 1(b) and 1(d) for p- and s-polarizations, respec-tively. Shown in Fig. 1(b) are the band dispersions aswell as their orbital characters, determined based on tightbinding calculation (See Supplementary). It is notewor-thy that the bands which cannot be identified with thecalculation results are surface states.

We performed temperature dependent experimentspresented to gain more information. Experiments weredone 1 hour after cleaving the sample at 30 K to removethe surface reconstruction effect [15]. The temperatureevolution of dxz/dyz splitting near the Γ point can beseen in the high symmetry cut and its second derivativedata shown in Figs. 2(a) and 2(b), respectively. Temper-ature dependent high symmetry cut data shows that theband dispersions around the Γ point hardly change ex-cept the thermal broadening. That is, dxz/yz hole bandsplitting near Γ, as indicated by the red dashed lines,appears to remain almost unchanged over the tempera-ture range we studied. The energy splitting size may beobtained from the temperature dependent energy distri-bution curves (EDCs) of the second derivative data in

Fig. 2(c). The EDCs are from k = 0.19A−1

as indicatedby the yellow dotted line in Fig. 1(b). Peak positions ofdxz and dyz hole bands are indicated by the arrows. Theband splitting at 30 K is about 50 meV and changes verylittle with the temperature, remaining finite even aboveTS . That is, the dxz/dyz hole band splitting near the Γpoint is not sensitive to the nematic phase transition.

In previous studies on other IBS, the dxz/dyz hole bandsplitting near the M point has been intensively studiedbecause of its large temperature dependence [6–8, 10–12, 15]. For that reason, we also focus on the tempera-ture dependence of the electronic structure near the Mpoint. Measurements were done with 21.2 eV photonenergy where the cross section is higher for M . Temper-ature dependent data and their second derivatives areplotted in Figs. 2(d) and 2(e). Split dxz and dyz holebands are observed at low temperatures as indicated byred dashed lines. In contrast to the temperature inde-pendent behavior near the Γ point, the splitting betweenthe two hole bands gradually decreases as the tempera-ture increases. The two bands finally merge each otherto a single band above TS . The temperature dependenceof band splitting may be observed more clearly in the

EDCs of second derivative data at k = −0.3A−1

in Fig.2(f). The splitting energy at a low temperature is about40 meV and vanishes above the nematic phase transitiontemperature TS .

Even though the temperature dependent behaviorstrongly indicates that the band splitting near M is due

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FIG. 2: (Color online). (a) Temperature dependent ARPES data and (b) its second derivative near the Γ point taken with 80eV photon. The red dashed lines indicate dispersions of dxz/yz bands. (c) Temperature dependent energy distribution curves

(EDCs) at k = 0.19A−1

, indicated by the yellow dashed line in Fig. 2(b). Peak positions of dxz and dyz are indicated byblack arrows. (d) Temperature dependent ARPES data and (e) its second derivative data near the M point taken with 21.2

eV photon energy, for which the cross section is higher. (f) Temperature dependent EDCs at k = −0.3A−1

, indicated by theyellow dashed line in Fig. 2(e).

to the nematic order, a true confirmation of the ne-matic nature should come from observation of depen-dent shift. In previous ARPES studies on detwinned IBS[6, 7, 11], nematic band shift has been observed in whichthe dyz (dxz) hole band from a single domain shifts up-ward (downward) along Γ-MX (MY ). Such band shiftslead to a simple energy splitting between the dxz and dyzhole bands in the twinned sample due to the mixed sig-nals from two perpendicularly arranged domains in the

nematic phase. It is reasonable to speculate that ob-served band splitting near the M point in our data isalso from the superposition of the dyz hole band alongΓ-MX and the dxz hole band along Γ-MY in LaFeAsO.This can be clarified through detwin experiments.

Detwinning was done by using a piezo stack basedstrain device which was adopted in previous FeSe studies[11]. Tensile strain is transmitted to the sample glued tothe piezo device when voltage is applied to the device.

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FIG. 3: (Color online). (a) Schematic illustration of experi-mental geometry. High symmetry cut of the (b) twinned and(c) detwinned sample along kx-direction near the MY point.The red and green dashed line indicated dispersion of dxz anddyz band, respectively. Tensile strain is transmitted to sampleby applying 150 V to the piezo strain device.

In our experiment, we applied 150 V to the piezo deviceat 200 K and cooled down the sample. Band dispersionnear the MY point along the kx-direction in twinned anddetwinned samples are presented in Figs. 3(b) and (c),respectively. In the detwin data, only the upper holeband (dyz) without the lower hole band (dxz) is seen incomparison to the twin data. Note that the band disper-sion in this experimental geometry is the same as the oneobtained along the kx-direction at MX due to the bandfolding; MY was chosen because the intensity is higher.Therefore, considering the normal state band dispersionsas well as our detwin experiment result, we conclude thatLaFeAsO also has nematic band shifts similar to otherIBS [20].

The discovery of the nematic band shift near M wastaken to be an evidence for a Ferro-orbital order whichin turn was considered to be the origin of the nematicphase. It is theoretically suggested that a nearly con-stant band splitting is expected in the entire Brillouinzone when Ferro-orbital order exists [21, 22]. However,ARPES results show that the band splitting has momen-tum dependence for all IBS systems including LaFeAsO,which excludes the Ferro-orbital scenario as the origin.Rather than the Ferro-orbital order, the instability forthe observed universal momentum dependent band split-ting should be the true origin of the nematic phase. Thereare proposals such as different form of orbital degree offreedom [23], Pomeranchuk instability [24] and spin de-gree of freedom [25–27] that require momentum depen-dence. Finding out which one of these is truly responsiblefor the nematic phase requires full understanding of thenematic electronic structure. As proposed very recently[11, 28], in addition to consideration of dxz and dyz holebands, evolution of dxz/dyz electron bands, spin orbitcoupling and role of dxy band should be elucidated toresolve the issue.

IV. CONCLUSION

In conclusion, we report the detailed electronic struc-ture of the nematic phase in LaFeAsO. We observe mo-mentum dependent dxz/dyz band splitting behavior nearthe Γ and M points in temperature dependent experi-ments. The splitting size near the M point decreases asthe temperature increases, while it is less temperaturesensitive near the Γ point. We confirmed the nematicnature of the band splitting near M by piezo detwinmethod. Our observation establishes the momentum de-pendent splitting as the universal behavior of the elec-tronic structure in the nematic phase of IBS. Our resultsuggests that instability causes the observed universalmomentum dependent band splitting should be the trueorigin of the nematic phase.

ACKNOWLEDGMENT

Authors would like to thank H. Pfau and Y. Ishidafor helpful discussions. This work is supported by IBS-R009-G2 through the IBS Center for Correlated Elec-tron Systems. Theoretical part was supported by grantsfrom CAS (XDB07000000). Part of this research usedBeamline 03U of the Shanghai Synchron Radiation Fa-cility, which is supported by ME2 project under contractNo. 11227902 from National Natural Science Founda-tion of China. The work at Pohang University of Sci-ence and Technology (POSTECH) was supported by IBS(no. IBS-R014-D1) and the NRF through the SRC (No.2018R1A5A6075964) and the Max Planck-POSTECHCenter (No. 2016K1A4A4A01922028). The work atIFW was supported by the (DFG) through the Prior-ity Program SPP 1458. The work at Korea AdvancedInstitute of Science and Technology (KAIST) was sup-ported by NRF through National R&D Program (No.2018K1A3A7A09056310), Creative Materials DiscoveryProgram (No. 2015M3D1A1070672), and Basic Sci-ence Resource Program (No. 2017R1A4A1015426, No.2018R1D1A1B07050869). The Advanced Light Source issupported by the Office of Basic Energy Sciences of theUS DOE under Contract No. DE-AC02-05CH11231.

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