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Scanning Tunneling Microscopy on heavy fermion metals Steffen Wirth MPI for Chemical Physics of Solids, Dresden, Germany. Introduction – heavy fermion metal YbRh 2 Si 2 – Scanning Tunneling M icroscopy STM / STS on YbRh 2 Si 2 – topography and surface structure - PowerPoint PPT Presentation
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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
Scanning Tunneling Microscopy on heavy fermion metals
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
Introduction
Quantum criticality in YbRh2Si2
Kondo physics at “high” T among heaviest HF metals (γ ≈ 1.6 J mol-1
K-2)
antiferromagnetic order ≤ 70 mK
quantum critical point
AF
YbRh2Si2
Custers et al.,Nature 424(2003) 524
Gegenwart et al., NJP 8 (2006) 171
T *
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
Introduction
Quantum criticality in YbRh2Si2
Kondo physics at “high” T among heaviest HF metals (γ ≈ 1.6 J mol-1
K-2)
antiferromagnetic order ≤ 70 mK
quantum critical point
~ T
~ 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)
Custers et al.,Nature 424(2003) 524
• Scanning Tunneling Spectroscopy Ernst et al., Nature 474, 362 (2011)
Kondo break-down, energy scale T *
reconstruction of Fermi surface involvement of 4f electrons
T *
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden Introduction to STM and STS
V
sample
tip
tunneling current
Scanning Tunneling Microscopy
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden Introduction to STM and STS
- 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
NbSe2
12 × 12 nm2, 380 mK, 0 TV
sample
tip
tunneling current
scan
Scanning Tunneling Microscopy
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden Introduction to STM and STS
• 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)
EF
LDOS
local density of states (DOS)
V > 0 V < 0
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden Introduction to STM and STS
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)
EF
LDOSV > 0 V < 0
dI / dV |V=V s (eVDC ) ≡ LDOS
low bias, “well behaved” tip, T(E,V,d) smooth
DC
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden Heavy fermion materials
• 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
Scanning Tunneling Microscopy on heavy fermion metals
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
FFT
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
STM on YbRh2Si2
2 x 2 nm2, height scale 25 pma = 4.01 Å c = 9.86 Å
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
STM on YbRh2Si2
cleaving: Yb-Si, termination unclearDanzenbächer et al., PRB 75, 045109 (2007)
2 x 2 nm2, height scale 25 pm
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Topography
→ very likely, a Si-terminated surface
excellent sample quality defect analysis
Δz
= 6
0 p
m
70 x 70 nm2
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Analysis of defects
→ very likely, a Si-terminated surface
excellent sample quality defect analysis
YbRh2Si2
Δz
= 6
0 p
m
70 x 70 nm2
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Analysis of defects
→ very likely, a Si-terminated surface
excellent sample quality defect analysis - Rh on Si site
YbRh2Si2
Δz
= 6
0 p
m
70 x 70 nm2
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Analysis of defects
→ very likely, a Si-terminated surface
excellent sample quality defect analysis - Rh on Si site - Si on Rh site
YbRh2Si2
Δz
= 6
0 p
m
70 x 70 nm2
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Analysis of defects
→ very likely, a Si-terminated surface
tunneling predominantly into conduction band, tunneling into 4f states neglected
70 x 70 nm2
Δz
= 6
0 p
m
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
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)
dI /
dV
(nS
)
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Crystal field effects
crystal field excitations at 17, 25 and 43 meV INS, Stockert et al., Physica B 378, 157 (2006)
• 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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Crystal field effects
crystal field excitations at 17, 25 and 43 meV INS, Stockert et al., Physica B 378, 157 (2006)
use of particle-hole symmetry
peak energies independent of T
-43 mV-27 mV
-17 mV
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
diluted magnetic impurities
Jun Kondo ‘63
spin-singlet ground state
strong correlations ( large)
Kondo interaction and STS
transport electron
scattered
electron
ξ
ξ
on-site Kondo effect: screening cloud
modified density of states ρ of the conduction band
local conductivity as measured by STS is changed accordingly
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Tunneling into two channels
local density of states:
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Tunneling into two channels
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)
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Tunneling into two channels
tunneling into - conduction band - 4f quasiparticle states Fano resonance
tunneling exclusively into conduction band covers essence of zero-bias dip
local density of states:
X
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)
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Tunneling into two channels
tunneling into - conduction band - 4f quasiparticle states Fano resonance
tunneling exclusively into conduction band covers essence of zero-bias dip
local density of states:
multi-level finite-U NCA(S. Kirchner)
4f DOS cal. spectra
X
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)
g(V,T )
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Tunneling into two channels
tunneling into - conduction band - 4f quasiparticle states Fano resonance
tunneling exclusively into conduction band covers essence of zero-bias dip
local density of states:
multi-level finite-U NCA(S. Kirchner)
4f DOS cal. spectra
X
g(V,T )
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)
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
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
rel.
de
pth
of
dip
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Kondo interaction
Renormalized Band Calculation; G. ZwicknaglS. Friedemann et al., PRB 82, 035103 (2010)
CEFCEF
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Kondo interaction
Renormalized Band Calculation; G. ZwicknaglS. Friedemann et al., PRB 82, 035103 (2010)
CEFCEF
analysis of peak width rather than peak height or position
K. Nagaoka et al., PRL 88, 077205 (2002)
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
Kondo interaction
Renormalized Band Calculation; G. ZwicknaglS. Friedemann et al., PRB 82, 035103 (2010)
CEFCEF
analysis of peak width rather than peak height or position
TKL = 30 ± 6 K K. Nagaoka et al., PRL 88, 077205 (2002)
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
maximum in ρ(T ), S(T ) at ~ 80 K local Kondo screening Kondo
dip
→ 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
*
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on YbRh2Si2
• 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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
Perspectives
Quantum criticality in YbRh2Si2
Kondo physics at “high” T
so far: How does the Kondo interaction develop ?
~ T
~ T 2AF
YbRh2Si2
B (T)
TLFLTN
T*
Custers et al.,Nature 424(2003) 524
Gegenwart et al.,Science 315(2007) 969
*
quantum critical point Kondo break-down, energy scale T
*
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
Perspectives
• UHV and in situ cleaving tools, preparation chamber, vibration and sound isolation
• low temperature, magnetic field
STM equipment
*
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
Perspectives
Low(er) temperature STS
• lower T → smaller width of crossover• signatures of Kondo breakdown ?
~ T
~ T 2AF
YbRh2Si2
• cleaving at low temperatures required
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
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 )
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
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
Lu Yb
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
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
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
Perspectives
Phase diagram
N.D. Mathur et al., 1998
CePd2Si2
unconventional superconductivity (pairing mechanism, order parameter)
magnetically mediated
J. Custers et al., 2003
~ T
~ T 2AF
YbRh2Si2
D.M. Broun, 2008
T
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden
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
xy
xxcotρ
ρθH
τeB
m
τωc
eff1
Scanning Tunneling Microscopy on heavy fermion metals
S. Wirth, MPI CPfS Dresden STM / STS on CeMIn5
STS on CeCoIn5
V = +14 mVIset = 340 pA
Vmod = 70 µV @ 180 Hz
Tc
Scanning Tunneling Microscopy on heavy fermion metals
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