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Confinement-Induced Vortex Phases in Superconductors

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

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Confinement-Induced Vortex Phases in Superconductors

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

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

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

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

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

  6. Superconductivity: Ginzburg-Landau Approach Integrating the 2nd G-L equation over an area S: , Φ being the magnetic flux crossing S where Condition on the phase φ (since ψ is a single-valued function): Fluxoid quantification: where Φ0 is the flux quantum:

  7. Superconductivity: Ginzburg-Landau Approach B > 0

  8. Superconductivity: Ginzburg-Landau Approach Φ = nΦ0 B > 0 vs=0

  9. Superconductivity: Ginzburg-Landau Approach Φ = nΦ0 B > 0 vs=0

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

  11. Superconductivity: Ginzburg-Landau Approach Φ = nΦ0 B > 0 vs=0 In type II superconductors (k>1) the Abrikosov vortex lattice forms, each vortex containing the flux quantum Φ0

  12. Superconductivity: Ginzburg-Landau Approach Individual Vortex Structure

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

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

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

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

  17. Scanning Tunneling Spectroscopy of Superconductors N S Vortex imaging in bulk superconductors by STS 2H-NbSe2 400 nm T = 4.2 K B = 1.0 T NB: The relation between the gap in the LDOS and Ψ(r) (GL) is not simple!

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

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

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

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

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

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

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

  25. Response of Confined Superconducting Condensate to an External Magnetic Field Bulk Pb (ξ0 = 80nm, λ0 = 50nm) – Type I, no vortices Our case: disordered Pb/Si interface limits the mean free path l: Dirty limit SC l≈2h=2x5.5nm = 11nm << ξ0 l = τvF Dirty limit : (l<<ξ) Additionally, in thin films (h<<λ): h Result: our Pb-island is the type II dirty limit SC; Magn. Field fully penetrates (Λ>>D), flux is not quantized.

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

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

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

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

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

  31. Zero Bias Gapped Area At the border Nif Naf Nif Naf Nouf Nouf

  32. Response of Confined Superconducting Condensate to an External Magnetic Field: Giant Vortex States

  33. Naf Nif In bulk superconductors at B=BC2: Nouf In our confined case (L=2): ! !

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

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

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

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

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

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

  40. Vortex Pool ZBC STS images (T=0.3K): 0.5T (≈15 Φ0) 0.2T (6 vortex) 0.1T (3 vortex) 3x2 vortices ! Lower ZBC – SC state Higher ZBC – vortex or normal state T. Cren et al., to be published

  41. Conclusions 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 BC2 in the bulk! At higher confinement Giant Vortex phase appears Confinement effects in “Vortex Pool”: Vortex core deformation, Vortex molecule formation, unexpected phase near BC Emerging of a New challenging field: Surface/Interface Superconductivity T. Cren et al. Phys. Rev. Lett. 102, 127005 (2009), T. Cren et al. Phys. Rev. Lett. 107, 097202 (2011)

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

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