1. Inhomogeneous electronic states in superconductors (Chapelier, Ioffe) How to disentangle the unavoidable atomic level inhomogeneity of real materials from the electronic inhomogeneity discussion-session

2. Maud Vinet Walter Escoffier Benjamin Sacépé Thomas Dubouchet Charlène Tonnoir Claude Chapelier CEA INAC-SPSMS-LaTEQS, Grenoble Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial)

3. Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial) I.STM/STS and usual inhomogeneous superconducting states II.Highly disordered superconductors III.Discussion

4. Coarse approach motor Coarse positioning X-Y table Sample holder Tip Piezo tube 10 cm Scanning Tunneling Microscopy Michael Schmid, TU Wien

5. P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996) Michael Schmid, TU Wien NbSe 2 Scanning Tunneling Microscopy

6. P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996) D. Roditchev’s group, http://ln-www.insp.upmc.fr/ Michael Schmid, TU Wien NbSe 2 Scanning Tunneling Microscopy

7. Scanning Tunneling Spectroscopy P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996) I V dI/dV NbSe 2 D. Roditchev’s group, http://ln-www.insp.upmc.fr/

8. Scanning Tunneling Spectroscopy P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996) I V dI/dV NbSe 2 D. Roditchev’s group, http://ln-www.insp.upmc.fr/ H. Hess et al., Physica B 169, 422 (1991)

9. I V dI/dV Scanning Tunneling Spectroscopy P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996) NbSe 2 D. Roditchev’s group, http://ln-www.insp.upmc.fr/ H. Hess et al., Physica B 169, 422 (1991)

10. I V dI/dV Scanning Tunneling Spectroscopy P.Mallet et al., J. Vac. Sci. Technol. B 14, 1070 (1996) NbSe 2 D. Roditchev’s group, http://ln-www.insp.upmc.fr/ I. Guillamon et al., Phys. Rev.B 77, 134405 (2008)

11. http://www.oettinger-physics.de/ Vortex NbSe 2 Sachdev & Zhang, Science

12. http://www.oettinger-physics.de/ Vortex H. Hess et al., Phys. Rev. Lett.. 62, 214 (1989) NbSe 2

13. http://www.oettinger-physics.de/ Vortex H. Hess et al., Phys. Rev. Lett.. 62, 214 (1989) NbSe 2

14. http://www.oettinger-physics.de/ Vortex NbSe 2 H. Hess et al., Physica B 169, 422 (1991)

15. http://www.oettinger-physics.de/ Vortex H. Hess et al., Physica B 169, 422 (1991) Ch. Renner et al., Phys. Rev. Lett. (1991) Nb 1-x Ta x Se 2

16. http://www.oettinger-physics.de/ Vortex J.E. Hoffman., Science 295, 466 (2002) Bi 2 Sr 2 CaCu 2 O 8+ 

17. Hybrid nanostructures N. Moussy et al., Europhys. Lett. 55, 861 (2001) M. Vinet et al., Phys. Rev. B 63, 165420 (2001) H. Le Sueur et al., Phys. Rev. Lett. 100, 197002 (2008)

18. Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial) I.STM/STS and usual inhomogeneous superconducting states II.Highly disordered superconductors III.Discussion

19. Superconductor-Insulator Transition Granular systemsHomogeneously disordered materials H.M. Jaeger, et al., Phys. Rev. B 34, 14920 (1986) D.B. Haviland, et al., Phys. Rev. Lett. 62, 2180 (1989) Gallium Bismuth

20. Superconductor-Insulator Transition TiN  Reactive sputter deposition of TiN films Homogeneously disordered ? N. Hadaceket al., Phys. Rev. B 69, 024505 (2004) 100 nm 10 nm

21. Superconductor-Insulator Transition TiN  100 nm 10 nm T (K) R (Ohms) Reactive sputter deposition of TiN films Granular ? Homogeneously disordered ? N. Hadaceket al., Phys. Rev. B 69, 024505 (2004)

22. Superconductor-Insulator Transition TiN  T (K) R (Ohms) Reactive sputter deposition of TiN films Granular ? Homogeneously disordered ? N. Hadaceket al., Phys. Rev. B 69, 024505 (2004) ≈ 80 × 80 × 2 nm ≈ 400 × 400 × 3 nm W. Escoffier et al.,Phys. Rev. Lett. 93, 217005 (2004) 100 nm 10 nm

23. Superconductor-Insulator Transition TiN  Reactive sputter deposition of TiN films Homogeneously disordered ? N. Hadaceket al., Phys. Rev. B 69, 024505 (2004) ≈ 80 × 80 × 2 nm ≈ 400 × 400 × 3 nm W. Escoffier et al.,Phys. Rev. Lett. 93, 217005 (2004) 100 nm 10 nm

24. M. Baklanov and A. Satta (IMEC) Superconductor-Insulator Transition TiN Atomic layer deposition of 5 nm thick TiN films

25. Increasing disorder Superconductor-Insulator transition Sacépé et al., Phys. Rev. Lett. 101, 157006 (2008) TiN

26. Superconductor-Insulator transition TiN λ Sacépé et al., Phys. Rev. Lett. 101, 157006 (2008) T c [K]Δ/T c Var. [%] 4.71.8--- 1.32.312 12.620 0.45450 A. Ghosal, M. Randeria, N. Trivedi, Phys. Rev. Lett. 81, 3940, (1998) Phys. Rev. B 65, 014501 (2001) M. Ma and P.A. Lee, Phys. Rev. B 32, 5658, (1985) A. Kapitulnik, G. Kotliar, Phys. Rev. Lett. 54, 473, (1985) M. Feigel’man et al., Phys. Rev. Lett. 98, 027001, (2007) M. Feigel’man et al., Ann. Phys. 325, 1390 (2010) M. A. Skvortsov et al., Phys. Rev. Lett. 95,057002, (2005)

27. Pseudogap B. Sacépé, et al., Nature Communications 1:140 (2010)

28. Superconducting fluctuations correction to the DOS Short-lived Cooper pairs above Tc A. Varlamov and V. Dorin, Sov. Phys. JETP 57, 1089, (1983) Pseudogap B. Sacépé, et al., Nature Communications 1:140 (2010)

29. Superconducting fluctuations correction to the DOS Short-lived Cooper pairs above Tc A. Varlamov and V. Dorin, Sov. Phys. JETP 57, 1089, (1983) Pseudogap B. Sacépé, et al., Nature Communications 1:140 (2010) R □ [kΩ] T c (R □ ) [K] T c (DOS) [K] 3.51.31.27 4.31.00.98 7.40.450.45 An extreme sensitivity to Tc

30. Very Low Temperature STM: a powerful probe for inhomogeneous superconducting states (tutorial) I.STM/STS and usual inhomogeneous superconducting states II.Highly disordered superconductors III.Discussion How to disentangle the unavoidable atomic level inhomogeneity of real materials from the electronic inhomogeneity ? Which inhomogeneities ? Down to which scale a real material must be considered granular or not ? What is a homogeneously disordered material ? How can we relate global macroscopic behavior (transport) and local signatures (STS) ?

31. Dilution fridge setup

32. Anomalous proximity effect Superconducting granular TiN films d S,N W. Escoffier et al., Phys. Rev. Lett. (2004) ≈ 80 × 80 × 2 nm ≈ 400 × 400 × 3 nm Theory : Zhang & Xiong, Physica C (2006)

33. Anomalous proximity effect Superconducting granular TiN films B. Sacépé (unpublished) 1500 nm x 1500 nm

34. Superconducting fluctuations quantum corrections

35. T c [K] 1.3 1 0.45 One parameter fit : T c Superconducting fluctuations quantum corrections