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Introduction – heavy fermion metal YbRh 2 Si 2

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

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Introduction – heavy fermion metal YbRh 2 Si 2

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  1. Scanning Tunneling Microscopy on heavy fermion metalsSteffen 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

  2. Thanks materials: Christoph Geibel Frank Steglich STM experim.: Stefan Ernst Cornelius Krellner Band Structure calculation: Gertrud Zwicknagl theory, NCA: Stefan Kirchner 115 materials: Joe Thompson, LANL Zach Fisk, UC Irvine Andrea Bianchi, U Montreal

  3. Quantum criticality in YbRh2Si2  Kondo physics at “high” T among heaviest HF metals (γ ≈ 1.6 Jmol-1K-2)  antiferromagnetic order ≤ 70 mK  quantum critical point T* Custers et al., Nature 424 (2003) 524 YbRh2Si2 Gegenwart et al., NJP 8 (2006) 171 AF

  4. ~T Quantum criticality in YbRh2Si2  Kondo physics at “high” T among heaviest HF metals (γ ≈ 1.6 Jmol-1K-2)  antiferromagnetic order ≤ 70 mK  quantum critical point T* Kondo break-down, energy scale T*  reconstruction of Fermi surface involvement of 4f electrons ~T2 Custers et al., Nature 424 (2003) 524 YbRh2Si2 • PhotoElectron Spectroscopy • de Haas-van Alphen effect • Hall effectPaschen et al., Nature 432, 881 (‘04) • Friedemann et al., PNAS 107, 14547 (2010) AF • Scanning Tunneling Spectroscopy • Ernst et al., Nature 474, 362 (2011)

  5. ScanningTunneling Microscopy tip V tunneling current sample

  6. ScanningTunneling Microscopy NbSe2 12 × 12 nm2, 380 mK, 0 T tip scan V tunneling current sample - 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

  7. ScanningTunneling Spectroscopy • keep tip at a predefined position (constant x and y) • open feedback loop of STM controller (constant z) • ramp the applied voltage  local density of states (DOS) V > 0 V < 0 LDOS EF tipsampletipsampletipsample thermal equilibrium positive sample bias negative sample bias zero bias: V = 0 (into empty states) (from occupied states)

  8. ScanningTunneling Spectroscopy dI/dV|V=V s(eVDC) ≡ LDOS low bias, “well behaved” tip, T(E,V,d) smooth DC V > 0 V < 0 LDOS EF tipsampletipsampletipsample thermal equilibrium positive sample bias negative sample bias zero bias: V = 0 (into empty states) (from occupied states)

  9. 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

  10. STM on YbRh2Si2 18 x 18 nm2 • samples cleaved • at T ~ 25 K • stable surfaces • over several weeks FFT

  11. STM on YbRh2Si2 2 x 2 nm2, height scale 25 pm a = 4.01 Å c = 9.86 Å

  12. STM on YbRh2Si2 2 x 2 nm2, height scale 25 pm cleaving: Yb-Si, termination unclear Danzenbächer et al., PRB 75, 045109 (2007)

  13. Topography 70x70 nm2 → very likely, a Si-terminated surface  excellent sample quality defect analysis Δz = 60 pm

  14. Analysis of defects 70x70 nm2 → very likely, a Si-terminated surface  excellent sample quality defect analysis YbRh2Si2 Δz = 60 pm

  15. Analysis of defects 70x70 nm2 → very likely, a Si-terminated surface  excellent sample quality defect analysis - Rh on Si site YbRh2Si2 Δz = 60 pm

  16. Analysis of defects 70x70 nm2 → very likely, a Si-terminated surface  excellent sample quality defect analysis - Rh on Si site - Si on Rh site YbRh2Si2 Δz = 60 pm

  17. Analysis of defects 70x70 nm2 → very likely, a Si-terminated surface  tunneling predominantly into conduction band, tunneling into 4f states neglected Δz = 60 pm

  18. 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 150x150 nm2

  19. STS on YbRh2Si2 • observations: • zero-bias dip of conductance • peaks at −17, −27, −43 mV • peak at −6 mV dI/dV (nS) T = 4.6 K V (mV)

  20. Crystal field effects crystal field excitations at 17, 25 and 43 meV INS, Stockert et al., Physica B 378, 157 (2006) -43 mV J= 7/2Hund’s rule multiplet -27 mV -17 mV

  21. Crystal field effects crystal field excitations at 17, 25 and 43 meV INS, Stockert et al., Physica B 378, 157 (2006) -43 mV J= 7/2Hund’s rule multiplet -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

  22. 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

  23. scattered electron transport electron Kondo interaction and STS on-site Kondo effect: screening cloud diluted magnetic impurities Jun Kondo ‘63 spin-singlet ground state strong correlations ( large)  modified density of states ρ of the conduction band  local conductivity as measured by STS is changed accordingly

  24. Tunneling into two channels local density of states:

  25. Tunneling into two channels 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 into - conduction band - 4f quasiparticle states Fano resonance

  26. Tunneling into two channels 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) X  tunneling into - conduction band - 4f quasiparticle states Fano resonance  tunneling exclusively into conduction band covers essence of zero-bias dip

  27. Tunneling into two channels 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) X  tunneling into - conduction band - 4f quasiparticle states Fano resonance  tunneling exclusively into conduction band covers essence of zero-bias dip g(V,T) V multi-level finite-U NCA (S. Kirchner) 4fDOS cal.spectra

  28. Tunneling into two channels 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) X  tunneling into - conduction band - 4f quasiparticle states Fano resonance  tunneling exclusively into conduction band covers essence of zero-bias dip g(V,T) V multi-level finite-U NCA (S. Kirchner) 4fDOS cal.spectra

  29. Zero-bias conductance dip  tunneling predominantly into conduction band  analysis of the depth of the Kondo dip  good agreement experiment& generalized NCA calculation conductance dip at zero bias rel. depth of dip dashed line: logarithmic decay T.A. Costi, PRL 85, 1504 (2000)

  30. 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

  31. 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)

  32. Kondo interaction Renormalized Band Calculation; G. Zwicknagl S. Friedemann et al., PRB 82, 035103 (2010) CEF CEF

  33. Kondo interaction Renormalized Band Calculation; G. Zwicknagl S. Friedemann et al., PRB 82, 035103 (2010) CEF CEF  analysis of peak width rather than peak height or position K. Nagaoka et al., PRL 88, 077205 (2002)

  34. Kondo interaction Renormalized Band Calculation; G. Zwicknagl S. Friedemann et al., PRB 82, 035103 (2010) CEF CEF  analysis of peak width rather than peak height or position TKL = 30 ± 6 K K. Nagaoka et al., PRL 88, 077205 (2002)

  35. Kondo interaction C = C(YbRh2Si2)  C(LuRh2Si2) ~ln(TKL/T) TKL =24K TKH~100K TKL = 20–30 K O. Trovarelli et al., PRL 85, 626 (2000)

  36. Kondo interaction * maximum in ρ(T), S(T) at ~80 K local Kondoscreening Kondodip → all CEF levelsCornut + 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

  37. 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

  38. ~T Quantum criticality in YbRh2Si2  Kondo physics at “high” T so far: How does the Kondo interaction develop? Custers et al., Nature 424 (2003) 524 YbRh2Si2  quantum critical point Kondo break-down,energy scale T* ~T2 AF * T* T (K) TLFL Gegenwart et al., Science 315 (2007) 969 TN B (T)

  39. STM equipment • UHV and in situ cleaving tools, • preparation chamber, • vibration and sound isolation • low temperature, magnetic field *

  40. ~T Low(er) temperature STS YbRh2Si2 ~T2 AF • lower T → smaller width of crossover • signatures of Kondo breakdown? • cleaving at low temperatures required

  41. Spatial dependence of spectroscopy T = 4.6 K • no local dependences of the • peak observed, neither at • –6 mV nor off the peak topography 800x720 pm2

  42. Spatial dependence of spectroscopy T = 4.6 K • no local dependences of the • peak observed, neither at • –6 mV nor off the peak indication for Si termination tunneling into conduction band spatially coherent state

  43. Quasiparticle interference T. Hanaguri et al., Nature Phys. 3 (´07) 865 • nature of many-body states: • FT of STS maps at • constant energy • successfully applied to • cuprate superconductors • but: 2D systems • SC in CeCoIn5: • dx2-y2 symmetry Ca2-xNaxCuO2Cl2 A. Akbari et al., PRB 84 (11) 134505 • YbRh2Si2: • tetragonal • Is there a unique • solution to FT ? Bi2Sr2CaCu2O8+ K. McElroy et al., Nature 422 (´03) 592

  44. Calculation of conductance curves g(V,T) • 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 V 4fDOS cal.spectra • NCA not applicable at low temperatures, • renormalized band structure calculations at T = 0 • other calculation schemes • e.g. NRG, quantum Monte Carlo simulation

  45. Substitution in YbRh2Si2 Custers et al., Nature 424 (´03) 524  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 T (K) B (T) Lu Yb Köhler et al., PRB 77 (´08) 104412

  46. Substitution in YbRh2Si2 Custers et al., Nature 424 (´03) 524  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 T (K) B (T) Volume

  47. N.D. Mathur et al., 1998 YbRh2Si2 D.M. Broun, 2008 CePd2Si2 ~T T ~T2 AF Phase diagram J. Custers et al., 2003 unconventional superconductivity (pairing mechanism, order parameter)  magnetically mediated

  48. Phase diagram of CeIrIn5 S. Nair et al., PRL 100 (‘08) 137003 Hall angle  fundamental property, directly related to and hence, charge carrier mobility

  49. STS on CeCoIn5 Tc V= +14 mV Iset = 340 pA Vmod = 70 µV @ 180 Hz

  50. 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

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