1. ECRYS 2011 Confinement-Induced Vortex Phases in Superconductors Institut des Nanosciences de Paris INSP, CNRS, Université Pierre et Marie Curie Paris 6, Paris, FRANCE Dimitri RODITCHEV with: Tristan Cren (researcher) Lise Serrier-Garcia (PhD) François Debontridder (Eng.)

2. ECRYS 2011 Vortex: An Universal Property of Quantum Condensates Scanning Tunneling Spectroscopy of Vortices Confinement-induced vortex configurations - Ultra-dense vortex lattice - Giant Vortex OUTLINE Conclusion T. Cren et al. Phys. Rev. Lett. 102, 127005 (2009), T. Cren et al. Phys. Rev. Lett. 107, 097202 (2011)

3. ECRYS 2011 Vortex: An Universal Property of Quantum Condensates Scanning Tunneling Spectroscopy of Vortices Confinement-induced vortex configurations - Ultra-dense vortex lattice - Giant Vortex OUTLINE Conclusion

4. ECRYS 2011 First image of Vortex, 1967 Vortex Physics in Rotating Quantum Condensates Vortex in ultracold condensate of atoms Vortex in superfluid He Superconductors (BCS)Cold atoms (BEC)Quantum liquids 3 vortices in SC nano-island STM/STS, INSP, 2009 100nm

5. ECRYS 2011 Superconductivity: Ginzburg-Landau Approach Boundary condition at the sample edge: Superconducting phase is described by macroscopic wave function: Two equations: (1) (2) where

6. ECRYS 2011 Superconductivity: Ginzburg-Landau Approach Fluxoid quantification: Integrating the 2 nd G-L equation over an area S: where, Φ being the magnetic flux crossing S where Φ 0 is the flux quantum: Condition on the phase φ (since ψ is a single-valued function):

7. ECRYS 2011 Superconductivity: Ginzburg-Landau Approach B > 0

8. ECRYS 2011 Superconductivity: Ginzburg-Landau Approach Φ = nΦ 0 v s =0 B > 0

9. ECRYS 2011 Superconductivity: Ginzburg-Landau Approach Φ = nΦ 0 v s =0 B > 0

10. ECRYS 2011 Superconductivity: Ginzburg-Landau Approach Two characteristic scales: coherence length ξ(T) and penetration depth λ(T) Influence of electron scattering: Additionally, in thin films (h<<λ): Mean free path l : l = τ v F G-L parameter separates the superconductors of type-I (k<1) from type-II (k>1) Dirty limit : (l<<ξ)

11. ECRYS 2011 Superconductivity: Ginzburg-Landau Approach Φ = nΦ 0 v s =0 B > 0 In type II superconductors (k>1) the Abrikosov vortex lattice forms, each vortex containing the flux quantum Φ 0

12. ECRYS 2011 Superconductivity: Ginzburg-Landau Approach Individual Vortex Structure

13. ECRYS 2011 D ~ ξ, ξ << λ Our motivation: Phase Diagram of Confined Superconductors - tiny magnetic response, - variations at nanometer scale D << λ

14. ECRYS 2011 V. Schweigert et al., Phys. Rev. Lett. 81, 2783 (1998) B. Baelus and F. Peeters, Phys. Rev. B 65, 104515 (2002) Superconducting nano-islands having a size of ~ξ should have peculiar properties due to the lateral confinement. Phase Diagram of Confined Superconductors Confined Vortex Configurations: Our Motivations

15. ECRYS 2011 Phase Diagram of Confined Superconductors Confined Vortex Configurations: Our Motivations

16. ECRYS 2011 Vortex: An Universal Property of Quantum Condensates Scanning Tunneling Spectroscopy of Vortices Confinement-induced vortex configurations - Ultra-dense vortex lattice - Giant Vortex OUTLINE Conclusion

17. ECRYS 2011 Scanning Tunneling Spectroscopy of Superconductors S N T = 4.2 K B = 1.0 T 400 nm 2H-NbSe 2 Vortex imaging in bulk superconductors by STS NB: The relation between the gap in the LDOS and Ψ(r) (GL) is not simple!

18. ECRYS 2011 Scanning Tunneling Spectroscopy of Superconductors S N Local Tunneling Spectra contain two important informations: Scale of ξ: Gap in dI/dV(V)Scale of λ: Effects of currents A. Anthore et al. PRL 90, 127001 (2003) A. Kohen et al. PRL 97, 027001 (2006) H. F. Hess et al. PRL 64, 2711 (1990)

19. ECRYS 2011 STM/STS in Paris (3 rd generation) UHV : p < 5x10 -11 mbar In-situ growth @ p < 3x10 -10 mbar Base T°: 0.285 mK Magn. Field: 0 –10 T

20. ECRYS 2011 Scanning Tunneling Spectroscopy of Superconductors S N T = 4.2 K B = 1.0 T STS: Vortex CORES (scale of ξ ) Field-sensitive methods: (scale of λ ) 400 nm

21. ECRYS 2011 Vortex: An Universal Property of Quantum Condensates Scanning Tunneling Spectroscopy of Vortices Confinement-induced vortex configurations - Ultra-dense vortex lattice - Giant Vortex OUTLINE Conclusion

22. ECRYS 2011 100nm Response of Confined Superconducting Condensate to an External Magnetic Field Samples: in-situ grown Pb-islands on 7x7 reconstructed Si(111) Si (111) + Pb-wetting layer (1-2 ML) Pb-nanocrystals (3-15 ML) Mono-atomic steps separating atomically flat terraces

23. ECRYS 2011 Samples: in-situ grown Pb-islands on 7x7 reconstructed Si(111) Response of Confined Superconducting Condensate to an External Magnetic Field Nif Naf Nouf

24. ECRYS 2011 Nif (111) Naf Samples: in-situ grown Pb-islands on 7x7 reconstructed Si(111) (111) Nif: D ≈ 140 nm h= 2.8nm – 10ML Naf: D ≈ 80-140 nm h= 2.3nm – 8ML Nouf: D ≈ 80 nm h= 2.3nm – 8ML Nouf Response of Confined Superconducting Condensate to an External Magnetic Field

25. ECRYS 2011 Bulk Pb (ξ 0 = 80nm, λ 0 = 50nm) – Type I, no vortices Our case: disordered Pb/Si interface limits the mean free path l: l ≈2 h =2x5.5nm = 11nm << ξ 0 Dirty limit SC Result: our Pb-island is the type II dirty limit SC; Magn. Field fully penetrates ( Λ >> D ), flux is not quantized. Additionally, in thin films (h<<λ): l = τ v F Dirty limit : (l<<ξ) h Response of Confined Superconducting Condensate to an External Magnetic Field

26. ECRYS 2011 ξ EFF ≈ 20-25 nm λ EFF ≈ 170 nm ≈ D Λ ≈ 12,000 nm >>D κ ≈ λ eff /ξ eff ≈ 8 Nif (111) Naf (111) Nouf Response of Confined Superconducting Condensate to an External Magnetic Field Result: our Pb-islands are the Type II dirty limit SCs; Magn. Field fully penetrates ( Λ >> D ), flux is not quantized.

27. ECRYS 2011 0.3K (T/Tc=1/20)0.8T : 10 times Hc(bulk Pb) Response of Confined Superconducting Condensate to an External Magnetic Field

28. ECRYS 2011 Response of Confined Superconducting Condensate to an External Magnetic Field 0.3K (T/Tc=1/20)0.8T : 10 times Hc(bulk Pb) STS: G.A. maps

29. ECRYS 2011 a)b) c) d) Model: A SC box with a Single Vortex inside (2/2)

30. ECRYS 2011 Response of Confined Superconducting Condensate to an External Magnetic Field

31. ECRYS 2011 Zero BiasGapped Area At the border Nif Naf Nouf Nif Naf Nouf

32. ECRYS 2011 At the border

33. ECRYS 2011 Response of Confined Superconducting Condensate to an External Magnetic Field: Giant Vortex States

34. ECRYS 2011 In bulk superconductors at B=B C2 : Nif Naf Nouf In our confined case (L=2): ! !

35. ECRYS 2011 Extras 1 – Vortex Pool: Playing with vortex core size and shape 2 – Quantum Well states and Superconductivity in Pb-Si system

36. ECRYS 2011 Vortex Pool Pb-Island on Si(111): Topographic STM Iimage T. Cren et al., to be published 160nm h=8.3nm h=2.6nm

37. ECRYS 2011 Vortex Pool Pb-Island on Si(111): T. Cren et al., to be published Sample Bias, mV dI/dV, arb. units B=0 T=0.3K BCS Fit: Δ=1.12meV Teff=0.39K Г=0 Topographic STM IimageLocal SIN Tunneling Spectrum

38. ECRYS 2011 Vortex Pool 0.1T – 3 Vortex T. Cren et al., to be published ZBC STS (T=0.3K): Lower ZBC – SC state Higher ZBC – vortex or normal state

39. ECRYS 2011 Vortex Pool 0.1T – 3 Vortex T. Cren et al., to be published ZBC STS (T=0.3K): Lower ZBC – SC state Higher ZBC – vortex or normal state

40. ECRYS 2011 A closer view.. Lower ZBC – SC state Higher ZBC – vortex or normal state 3x2 vortices ! ZBC STS images (T=0.3K): Vortex Pool 0.2T (6 vortex) 0.1T (3 vortex) T. Cren et al., to be published Core Deformation !

41. ECRYS 2011 0.5T (≈15 Φ 0 ) Lower ZBC – SC state Higher ZBC – vortex or normal state 3x2 vortices ! ZBC STS images (T=0.3K): Vortex Pool 0.2T (6 vortex) 0.1T (3 vortex) T. Cren et al., to be published

42. ECRYS 2011 Vortex phases in strongly confining geometries: Individual and atomically perfect samples are now experimentally accessible Coherence length and penetration depth are strongly affected by geometry Vortex Box: Vortex looses its “Flux Quantum” meaning: Only “Phase” and “Currents” remain relevant. Magnetic energy is not relevant anymore: Superconductors start behaving as other (neutral) quantum condensates (cold atoms, quantum liquids, polaritons etc.) Multi-Vortex Configurations: Confinement results in super-dense vortex configurations: The vortex-vortex distance observed up to 3 times shorter than at B C2 in the bulk! At higher confinement Giant Vortex phase appears Confinement effects in “Vortex Pool”: Vortex core deformation, Vortex molecule formation, unexpected phase near B C Emerging of a New challenging field: Surface/Interface Superconductivity Conclusions T. Cren et al. Phys. Rev. Lett. 102, 127005 (2009), T. Cren et al. Phys. Rev. Lett. 107, 097202 (2011)

43. ECRYS 2011 STM/STS team at the Institute for Nano-Science of Paris http://www.insp.jussieu.fr/-Dispositifs-quantiques-controles-.html