1. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Magnetotransport in CeMIn 5 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 Microscopy STM / STS on YbRh 2 Si 2 – topography and surface structure – crystal field excitations – hybridization and Kondo effect Perspectives – extending temperature & field range – quasi-particle interference – doped YbRh 2 Si 2 -based materials – other materials: HF superconductors

2. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Introduction Thanks STM experim.: Stefan Ernst theory, NCA: Stefan Kirchner Frank Steglich Band Structure calculation: Gertrud Zwicknagl materials: Christoph Geibel Cornelius Krellner 115 materials: Joe Thompson, LANL Zach Fisk, UC Irvine Andrea Bianchi, U Montreal

3. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Introduction Quantum criticality in YbRh 2 Si 2  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 YbRh 2 Si 2 Custers et al., Nature 424 (2003) 524 Gegenwart et al., NJP 8 (2006) 171 T *T *

4. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Introduction Quantum criticality in YbRh 2 Si 2  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 2 AF YbRh 2 Si 2 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 *T *

5. 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

6. 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 E F NbSe 2 12 × 12 nm 2, 380 mK, 0 T V sample tip tunneling current scan Scanning Tunneling Microscopy

7. 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 bias zero bias: V = 0 (into empty states) (from occupied states) EFEF LDOS  local density of states (DOS) V > 0V < 0

8. 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 bias zero bias: V = 0 (into empty states) (from occupied states) EFEF LDOS V > 0V < 0 dI / dV | V=V   s (eV DC ) ≡ LDOS low bias, “well behaved” tip, T(E,V,d) smooth DC

9. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Introduction to STM and STS  vibration isolation  UHV, LHe-temperatures  in situ low temperature cleaving

10. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Heavy fermion materials Introduction – heavy fermion metal YbRh 2 Si 2 – Scanning Tunneling Microscopy STM / STS on YbRh 2 Si 2 – topography and surface structure – crystal field excitations – hybridization and Kondo effect Perspectives – extending temperature & field range – quasi-particle interference – doped YbRh 2 Si 2 -based materials – other materials: HF superconductors

11. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 STM on YbRh 2 Si 2 18 x 18 nm 2 samples cleaved at T ~ 25 K stable surfaces over several weeks FFT

12. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 STM on YbRh 2 Si 2 2 x 2 nm 2, height scale 25 pm a = 4.01 Å c = 9.86 Å

13. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 STM on YbRh 2 Si 2 cleaving: Yb-Si, termination unclear Danzenbächer et al., PRB 75, 045109 (2007) 2 x 2 nm 2, height scale 25 pm

14. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Topography → very likely, a Si-terminated surface  excellent sample quality defect analysis Δz = 60 pm 70 x 70 nm 2

15. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Analysis of defects → very likely, a Si-terminated surface  excellent sample quality defect analysis YbRh 2 Si 2 Δz = 60 pm 70 x 70 nm 2

16. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Analysis of defects → very likely, a Si-terminated surface  excellent sample quality defect analysis - Rh on Si site YbRh 2 Si 2 Δz = 60 pm 70 x 70 nm 2

17. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Analysis of defects → very likely, a Si-terminated surface  excellent sample quality defect analysis - Rh on Si site - Si on Rh site YbRh 2 Si 2 Δz = 60 pm 70 x 70 nm 2

18. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Analysis of defects → very likely, a Si-terminated surface  tunneling predominantly into conduction band, tunneling into 4f states neglected 70 x 70 nm 2 Δz = 60 pm

19. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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 nm 2

20. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 STS on YbRh 2 Si 2 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)

21. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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

22. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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: YbRh 2 Si 2 is a hole system with valency ~2.9  J = 7 / 2 Hund’s rule multiplet -43 mV -27 mV -17 mV

23. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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

24. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2  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

25. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Tunneling into two channels local density of states:

26. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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 URu 2 Si 2 : - A.R. Schmidt et al., Nature 465, 570 (‘10) - P. Aynajian et al., PNAS 107, 10383 (‘10)

27. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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 URu 2 Si 2 : - A.R. Schmidt et al., Nature 465, 570 (‘10) - P. Aynajian et al., PNAS 107, 10383 (‘10)

28. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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 URu 2 Si 2 : - A.R. Schmidt et al., Nature 465, 570 (‘10) - P. Aynajian et al., PNAS 107, 10383 (‘10) g(V,T )g(V,T )

29. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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 )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 URu 2 Si 2 : - A.R. Schmidt et al., Nature 465, 570 (‘10) - P. Aynajian et al., PNAS 107, 10383 (‘10)

30. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 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. depth of dip

31. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2  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

32. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2  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 T KL = 29 K in YbRh 2 Si 2 Köhler et al., PRB 77, 104412 (2008) Kondo interaction

33. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Kondo interaction Renormalized Band Calculation; G. Zwicknagl S. Friedemann et al., PRB 82, 035103 (2010) CEF

34. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Kondo interaction Renormalized Band Calculation; G. Zwicknagl S. Friedemann et al., PRB 82, 035103 (2010) CEF  analysis of peak width rather than peak height or position K. Nagaoka et al., PRL 88, 077205 (2002)

35. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Kondo interaction Renormalized Band Calculation; G. Zwicknagl S. Friedemann et al., PRB 82, 035103 (2010) CEF  analysis of peak width rather than peak height or position T KL = 30 ± 6 K K. Nagaoka et al., PRL 88, 077205 (2002)

36. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Kondo interaction  C = C(YbRh 2 Si 2 )  C(LuRh 2 Si 2 ) T KL = 20 – 30 K ~ ln(T KL / T ) T KL = 24 K O. Trovarelli et al., PRL 85, 626 (2000) T KH ~ 100 K

37. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2  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 = T KL of lowest-lying Kramers doublet peak at –6 mV Kondo interaction *

38. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on YbRh 2 Si 2 Introduction – heavy fermion metal YbRh 2 Si 2 – Scanning Tunneling Microscopy STM / STS on YbRh 2 Si 2 – topography and surface structure – crystal field excitations – hybridization and Kondo effect Perspectives – extending temperature & field range – quasi-particle interference – doped YbRh 2 Si 2 -based materials – other materials: HF superconductors

39. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Perspectives Quantum criticality in YbRh 2 Si 2  Kondo physics at “high” T so far: How does the Kondo interaction develop ?  ~ T  ~ T 2 AF YbRh 2 Si 2 B (T) T LFL TNTN T* Custers et al., Nature 424 (2003) 524 Gegenwart et al., Science 315 (2007) 969 *  quantum critical point Kondo break-down, energy scale T *

40. 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 *

41. 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 2 AF YbRh 2 Si 2 cleaving at low temperatures required

42. 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 pm 2 topography T = 4.6 K

43. 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

44. 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 Bi 2 Sr 2 CaCu 2 O 8+  K. McElroy et al., Nature 422 (´03) 592 Ca 2-x Na x CuO 2 Cl 2 YbRh 2 Si 2 : tetragonal  Is there a unique solution to FT ? but: 2D systems SC in CeCoIn 5 : d x 2 -y 2 symmetry A. Akbari et al., PRB 84 (11) 134505

45. 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 )g(V,T )

46. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Perspectives Substitution in YbRh 2 Si 2  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 B (T) Custers et al., Nature 424 (´03) 524 Köhler et al., PRB 77 (´08) 104412 Lu Yb

47. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Perspectives Substitution in YbRh 2 Si 2  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 B (T) Custers et al., Nature 424 (´03) 524 Volume

48. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Perspectives Phase diagram N.D. Mathur et al., 1998 CePd 2 Si 2  unconventional superconductivity (pairing mechanism, order parameter)  magnetically mediated J. Custers et al., 2003  ~ T  ~ T 2 AF YbRh 2 Si 2 D.M. Broun, 2008 T

49. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Perspectives Phase diagram of CeIrIn 5 Hall angle  fundamental property, directly related to and hence, charge carrier mobility S. Nair et al., PRL 100 (‘08) 137003

50. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden STM / STS on CeMIn 5 STS on CeCoIn 5 V = +14 mV I set = 340 pA V mod = 70 µV @ 180 Hz TcTc

51. Scanning Tunneling Microscopy on heavy fermion metals S. Wirth, MPI CPfS Dresden Summary Summary  Topography on YbRh 2 Si 2 : - perfect low-T cleave - Si terminated  Spectroscopy on YbRh 2 Si 2 : - 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