Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Magnetotransport in...

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Scanning Tunneling Microscopy on heavy fermion metals

S. Wirth, MPI CPfS Dresden Magnetotransport in CeMIn5Scanning Tunneling Microscopy on heavy fermion metals

Steffen WirthMPI for Chemical Physics of Solids, Dresden, Germany

• Introduction – heavy fermion metal YbRh2Si2

– Scanning Tunneling Microscopy

• STM / STS on YbRh2Si2 – topography and surface structure– crystal field excitations – hybridization and Kondo effect

• Perspectives – extending temperature & field range – quasi-particle interference – doped YbRh2Si2-based materials

– other materials: HF superconductors

S. Wirth, MPI CPfS Dresden

Introduction

Thanks

STMexperim.:

Stefan Ernst

theory,NCA:StefanKirchner

Frank Steglich

BandStructurecalculation:Gertrud Zwicknagl

materials:

Christoph Geibel

Cornelius Krellner

115 materials:Joe Thompson, LANL Zach Fisk, UC Irvine

Andrea Bianchi, U Montreal

Introduction

Quantum criticality in YbRh2Si2

Kondo physics at “high” T among heaviest HF metals (γ ≈ 1.6 J mol-1

antiferromagnetic order ≤ 70 mK

quantum critical point

YbRh2Si2

Custers et al.,Nature 424(2003) 524

Gegenwart et al., NJP 8 (2006) 171

Introduction

Kondo physics at “high” T among heaviest HF metals (γ ≈ 1.6 J mol-1

antiferromagnetic order ≤ 70 mK

quantum critical point

~ T 2AF

YbRh2Si2

• PhotoElectron Spectroscopy

• de Haas-van Alphen effect

• Hall effect Paschen et al., Nature 432, 881 (‘04) Friedemann et al., PNAS 107, 14547 (2010)

• Scanning Tunneling Spectroscopy Ernst et al., Nature 474, 362 (2011)

Kondo break-down, energy scale T *

reconstruction of Fermi surface involvement of 4f electrons

S. Wirth, MPI CPfS Dresden Introduction to STM and STS

sample

tunneling current

Scanning Tunneling Microscopy

- atomic resolution due to exponential dependence of I on tip-sample distance

- images: scanning the tip at constant height or constant current

- images correspond to planes of constant DOS at EF

12 × 12 nm2, 380 mK, 0 TV

sample

tunneling current

Scanning Tunneling Microscopy

• keep tip at a predefined position (constant x and y)

• open feedback loop of STM controller (constant z)

• ramp the applied voltage

Scanning Tunneling Spectroscopy

tip sample tip sample tip sample

thermal equilibrium positive sample bias negative sample biaszero bias: V = 0 (into empty states) (from occupied states)

local density of states (DOS)

V > 0 V < 0

Scanning Tunneling Spectroscopy

tip sample tip sample tip sample

thermal equilibrium positive sample bias negative sample biaszero bias: V = 0 (into empty states) (from occupied states)

LDOSV > 0 V < 0

dI / dV |V=V s (eVDC ) ≡ LDOS

low bias, “well behaved” tip, T(E,V,d) smooth

S. Wirth, MPI CPfS Dresden Heavy fermion materials

S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2

STM on YbRh2Si218 x 18 nm2

• samples cleaved at T ~ 25 K

• stable surfaces over several weeks

STM on YbRh2Si2

2 x 2 nm2, height scale 25 pma = 4.01 Å c = 9.86 Å

STM on YbRh2Si2

cleaving: Yb-Si, termination unclearDanzenbächer et al., PRB 75, 045109 (2007)

2 x 2 nm2, height scale 25 pm

Topography

→ very likely, a Si-terminated surface

excellent sample quality defect analysis

70 x 70 nm2

Analysis of defects

excellent sample quality defect analysis

YbRh2Si2

70 x 70 nm2

Analysis of defects

excellent sample quality defect analysis - Rh on Si site

YbRh2Si2

70 x 70 nm2

Analysis of defects

excellent sample quality defect analysis - Rh on Si site - Si on Rh site

YbRh2Si2

70 x 70 nm2

Analysis of defects

tunneling predominantly into conduction band, tunneling into 4f states neglected

70 x 70 nm2

Comparison to chemical analysis homogeneity range:

40.0 – 40.2 at% Rh

best samples (RRR): Rh excess

topography: 380 excess Rh out of 140,000 atoms → 40.12 at% WDXS: 40.16 ± 0.12 at% Rh

150 x 150 nm2

STS on YbRh2Si2

T = 4.6 K

observations:

• zero-bias dip of conductance

• peaks at −17, −27, −43 mV

• peak at −6 mV

V (mV)

Crystal field effects

crystal field excitations at 17, 25 and 43 meV INS, Stockert et al., Physica B 378, 157 (2006)

J = 7/2 Hund’s rule multiplet

-43 mV-27 mV

-17 mV

• first time that CEF excitations are observed in STS

• CEF excitations are a true bulk property

• CEF excitations originate in Yb → yet another indication for Si-terminated surface

• asymmetry: YbRh2Si2 is a hole system with valency ~2.9

J = 7/2 Hund’s rule multiplet

-43 mV-27 mV

-17 mV

use of particle-hole symmetry

peak energies independent of T

-43 mV-27 mV

-17 mV

diluted magnetic impurities

Jun Kondo ‘63

spin-singlet ground state

strong correlations ( large)

Kondo interaction and STS

transport electron

scattered

electron

on-site Kondo effect: screening cloud

modified density of states ρ of the conduction band

local conductivity as measured by STS is changed accordingly

Tunneling into two channels

local density of states:

tunneling into - conduction band - 4f quasiparticle states Fano resonance

local density of states: Theory: - M. Maltseva et al., PRL 103, 206402 (‘09) - J. Figgins, D. Morr, PRL 104, 187202

(‘10) - P. Wölfle et al., PRL 105, 246401 (‘10)

Experiments on URu2Si2: - A.R. Schmidt et al., Nature 465, 570 (‘10) - P. Aynajian et al., PNAS 107, 10383 (‘10)

tunneling exclusively into conduction band covers essence of zero-bias dip

Theory: - M. Maltseva et al., PRL 103, 206402 (‘09) - J. Figgins, D. Morr, PRL 104, 187202

(‘10) - P. Wölfle et al., PRL 105, 246401 (‘10)

multi-level finite-U NCA(S. Kirchner)

4f DOS cal. spectra

(‘10) - P. Wölfle et al., PRL 105, 246401 (‘10)

g(V,T )

multi-level finite-U NCA(S. Kirchner)

4f DOS cal. spectra

g(V,T )

(‘10) - P. Wölfle et al., PRL 105, 246401 (‘10)

Zero-bias conductance dip

tunneling predominantly into conduction band

analysis of the depth of the Kondo dip

dashed line: logarithmic decay T.A. Costi, PRL 85, 1504 (2000)

good agreement experiment & generalized NCA calculation

conductance dip at zero bias

criteria: no inflection point within -20 – 0 mV, fulfilled for T ≥ 30 K curves at T ≥ 30 K used as “background”

Gaussian peak

Kondo interaction

criteria: no inflection point within -20 – 0 mV, fulfilled for T ≥ 30 K curves at T ≥ 30 K used as “background”

Gaussian peak, suppressed at T ≈ 27 K, from thermopower measurements TKL = 29 K in YbRh2Si2

Köhler et al., PRB 77, 104412 (2008)

Kondo interaction

Renormalized Band Calculation; G. ZwicknaglS. Friedemann et al., PRB 82, 035103 (2010)

CEFCEF

Kondo interaction

CEFCEF

analysis of peak width rather than peak height or position

K. Nagaoka et al., PRL 88, 077205 (2002)

Kondo interaction

CEFCEF

analysis of peak width rather than peak height or position

TKL = 30 ± 6 K K. Nagaoka et al., PRL 88, 077205 (2002)

Kondo interaction

C = C(YbRh2Si2) C(LuRh2Si2)

TKL = 20 – 30 K

~ ln(TKL / T )

TKL = 24 K

O. Trovarelli et al., PRL 85, 626 (2000)

TKH ~ 100 K

maximum in ρ(T ), S(T ) at ~ 80 K local Kondo screening Kondo

→ all CEF levels Cornut + Coqblin 1972

upon cooling, 4f e– condense into CEF Kramers doublet ground state

→ formation of Kondo lattice below ~30 K = TKL of lowest-lying Kramers doublet peak at –6 mV

Kondo interaction

Perspectives

Kondo physics at “high” T

so far: How does the Kondo interaction develop ?

~ T 2AF

YbRh2Si2

TLFLTN

Gegenwart et al.,Science 315(2007) 969

quantum critical point Kondo break-down, energy scale T

Perspectives

• UHV and in situ cleaving tools, preparation chamber, vibration and sound isolation

• low temperature, magnetic field

STM equipment

Perspectives

Low(er) temperature STS

• lower T → smaller width of crossover• signatures of Kondo breakdown ?

~ T 2AF

YbRh2Si2

• cleaving at low temperatures required

Perspectives

Spatial dependence of spectroscopy

• no local dependences of the peak observed, neither at –6 mV nor off the peak

800 x 720 pm2

T = 4.6 K

Perspectives

Spatial dependence of spectroscopy

indication for Si termination tunneling into conduction band

spatially coherent state

• no local dependences of the peak observed, neither at –6 mV nor off the peak

T = 4.6 K

Perspectives

Quasiparticle interference

• nature of many-body states: FT of STS maps at constant energy

• successfully applied to cuprate superconductors

T. Hanaguri et al.,Nature Phys. 3 (´07) 865

Bi2Sr2CaCu2O8+

K. McElroy et al.,Nature 422 (´03) 592

Ca2-xNaxCuO2Cl2

• YbRh2Si2: tetragonal

Is there a unique solution to FT ?

• but: 2D systems

• SC in CeCoIn5: dx2-y2 symmetry

A. Akbari et al.,PRB 84 (11) 134505

Perspectives

Calculation of conductance curves

• so far: multi-level, finite-U NCA

but: level-splitting not included

• code under development that explicitly takes into account the four levels

but: many open parameters

• NCA not applicable at low temperatures, renormalized band structure calculations at T = 0

other calculation schemes e.g. NRG, quantum Monte Carlo simulation

4f DOS cal. spectra

g(V,T )

Perspectives

Substitution in YbRh2Si2

possible on each lattice site: - Ge Si: Si-terminated?

- Lu Yb: different cleave? A.R. Schmidt et al., Nature 465, 570

diluted Kondo lattice

- Co,Ir Rh: energy scales S. Friedemann et al., Nature Phys. 5 (2009) 465

Custers et al.,Nature 424 (´03) 524

Köhler et al., PRB 77 (´08) 104412

Perspectives

Substitution in YbRh2Si2

possible on each lattice site: - Ge Si: Si-terminated?

- Lu Yb: different cleave? A.R. Schmidt et al., Nature 465, 570

diluted Kondo lattice

- Co,Ir Rh: energy scales S. Friedemann et al., Nature Phys. 5 (2009) 465

Custers et al.,Nature 424 (´03) 524

Volume

Perspectives

Phase diagram

N.D. Mathur et al., 1998

CePd2Si2

unconventional superconductivity (pairing mechanism, order parameter)

magnetically mediated

J. Custers et al., 2003

~ T 2AF

YbRh2Si2

D.M. Broun, 2008

Perspectives

Phase diagram of CeIrIn5

Hall angle

fundamental property, directly related to and hence, charge carrier mobility

S. Nair et al., PRL 100 (‘08) 137003

xxcotρ

S. Wirth, MPI CPfS Dresden STM / STS on CeMIn5

STS on CeCoIn5

V = +14 mVIset = 340 pA

Vmod = 70 µV @ 180 Hz

S. Wirth, MPI CPfS Dresden Summary

Summary

Topography on YbRh2Si2: - perfect

low-T cleave

- Si terminated

Spectroscopy on YbRh2Si2: - crystalline electric field (CEF) exitations

- single-ion Kondo interaction at 80 – 100 K experiment calculations

- Kondo lattice coherence below ~30 K

exciting prospects: - lower T → signatures of quantum critical. - substituted materials → energy scales, FT-STS - heavy fermion superconductors

Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Magnetotransport in...

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