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Localization of preformed Cooper-pairs in disordered superconductors

Benjamin Sacépé. Localization of preformed Cooper-pairs in disordered superconductors. Institut Néel, CNRS & Université Joseph Fourier, Grenoble. Lorentz Center, Leiden 2011. Benjamin Sacépé. Localization of preformed Cooper-pairs in disordered superconductors.

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Localization of preformed Cooper-pairs in disordered superconductors

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  1. Benjamin Sacépé Localization of preformed Cooper-pairs in disordered superconductors Institut Néel, CNRS & Université Joseph Fourier, Grenoble Lorentz Center, Leiden 2011

  2. Benjamin Sacépé Localization of preformed Cooper-pairs in disordered superconductors Institut Néel, CNRS & Université Joseph Fourier, Grenoble Thomas Dubouchet, Claude Chapelier, Marc Sanquer CEA Grenoble Maoz Ovadia, Dan Shahar Weizmann Institute of Science, Rehovot M. Feigel’man L.D. Landau Institut for Theoretical Phyiscs, Moscow L. Ioffe Rutgers University, Piscataway Lorentz Center, Leiden 2011

  3. Superconductor-Insulator Transition (SIT) Quench condensed Bismuth Main ingredients : d = • Disorder localization • Attractive pairing superconducting phase • Coulomb interaction competes with pairing • Reduced dimensionality affects 1,2 and 3 d = D.B. Haviland, Y. Lui, A.M. Goldman,PRL(‘89)

  4. Magnetic field-tuned SIT Amorphous indium oxide V.F.Gantmakher et al., JETP 82, 951 (1996) G. Sambandamurthy, et al. PRL 94, 017003, (2005) For similar results in TiN films see : T. Baturina, et al. PRL (2007)

  5. 0.20K Magnetic field-tuned SIT Superconductor

  6. 0.20K Magnetic field-tuned SIT Superconductor Insulator Positive magnetoresistance at low field : Superconducting correlations in insulators !?

  7. 0.20K Magnetic field-tuned SIT Superconductor Insulator Positive magnetoresistance at low field : Superconducting correlations in insulators !? « Insulating correlations » in superconductors ???

  8. mK-STM setup : tunneling spectroscopy C. Chapelier’s setup, CEA Grenoble 50mK< T< 6K Cryostat : inverted dilution • Combined transport and spectroscopy measurements

  9. 1 mm Amorphous Indium Oxyde (a-InOx) Thickness : 15 nm (blue) and 30 nm (red)  3D regime InO#2 InO#1 Samples : e-gun evaporation onto Si/SiO2 substrate of high purity In2O3 under O2 pressure

  10. 1 mm Amorphous Indium Oxyde (a-InOx) Thickness : 15 nm (blue) and 30 nm (red)  3D regime InO#2 InO#1 Samples : e-gun evaporation onto Si/SiO2 substrate of high purity In2O3 under O2 pressure V.F.Gantmakher et al., JETP 82, 951 (1996)

  11. Tunneling spectroscopy of amorphous indium oxyde Typical spectrum measured at 50 mK InO#1 Fit : s-wave BCS density-of-states

  12. Inhomogeneities of Δ(r) Map of the spectral gap Gaussian distribution For similar results in TiN and NbN films see : B. Sacépé, et al. PRL 101, 157006 (2008) M. Mondal, et al. PRL 106, 047001 (2011)

  13. G, Normalized G, Normalized Inhomogeneities of Δ(r) Spectra measured at different locations (T=50mK) Gaussian distribution For similar results in TiN and NbN films see : B. Sacépé, et al. PRL 101, 157006 (2008) M. Mondal, et al. PRL 106, 047001 (2011)

  14. Fluctuations of Δ(r) and superconducting transition BCS ratio Δ/Tc =1.76 ?

  15. Fluctuations of Δ(r) and superconducting transition • Definition of Tc : zero-resistance state (macroscopic phase coherence)

  16. G, Normalized G, Normalized Fluctuations of the BCS peaks Fluctuations of peak heights !

  17. Fluctuations of the BCS peaks

  18. Fluctuations of the BCS peaks

  19. Fluctuations of the BCS peaks

  20. Extreme case : « Insulating » gap Spectra measured at different locations (T=50mK)

  21. High disorder sample Let’s approach the SIT InO#2 InO#1 Sample InO#2 : disorder  2 G, Normalized G, Normalized

  22. Let’s approach the SIT InO#2 InO#1 Increase of disorder InO#1 Tc ~ 1.7 K resistivity × 2 InO#2 Tc ~ 1.3 K • Proliferation of gaps without peaks

  23. λ λ Superconductivity and disorder Role of Spatial Amplitude Fluctuations in Highly Disordered s-Wave Superconductor A. Ghosal, M. Randeria, N. Trivedi,PRL 81, 3940, (1998) and PRB 65, 014501 (2001) • With increasing disorder : • Superconductivity becomes « granular-like » • Spectral gap remains finite even at large disorder • Spectral gap is NOT anymore the SC order parameter

  24. λ λ Superconductivity and disorder Role of Spatial Amplitude Fluctuations in Highly Disordered s-Wave Superconductor A. Ghosal, M. Randeria, N. Trivedi,PRL 81, 3940, (1998) and PRB 65, 014501 (2001) • Insulating gap induced by pairing interaction M. Ma, and P. A. Lee,PRB 32, 5658, (1985) M. Feigel’man, et al., PRL 98, 027001, (2007) M. Feigel’man, et al,Ann. Phys.325, 1390 (2010) M. Feigel’man, et al,PRB (2010)

  25. Insulating gap due to pairing P. W. Anderson, J. Phys. (Paris) Colloq. 37, C4-339 (1976) M. Ma, and P. A. Lee,PRB 32, 5658, (1985) K. A. Matveev and A. Larkin,PRL. 78, 3749, (1997) A. Ghosal, et al.PRL 81, 3940, (1998) and PRB 65, 014501 (2001) M. Feigel’man, et al. PRL 98, 027001, (2007) M. Feigel’man, et al.Ann. Phys.325, 1390 (2010) M. Feigel’man, et al.PRB82, 184534 (2010) Reduced BCS Hamiltonian built on eigenstates of the Anderson problem with In the high-disorder regime when In the lowest order:

  26. λ λ Superconductivity and disorder Role of Spatial Amplitude Fluctuations in Highly Disordered s-Wave Superconductor A. Ghosal, M. Randeria, N. Trivedi,PRL 81, 3940, (1998) and PRB 65, 014501 (2001) • Insulating gap induced by pairing interaction M. Ma, and P. A. Lee,PRB 32, 5658, (1985) M. Feigel’man, et al., PRL 98, 027001, (2007) M. Feigel’man, et al,Ann. Phys.325, 1390 (2010) M. Feigel’man, et al,PRB (2010)

  27. Superconductivity and disorder Recent QMC simulations K. Bouadim, Y. Loh, M. Randeria, N. Trivedi,arXiv:1011.3275 Insulator Disorder SC

  28. Pairing gap in the insulator resistivity × 2 • Proliferation of incoherent –localized— Cooper-pairs when approaching the SIT

  29. Pairing gap in the insulator Simulations on the Bethe lattice Lev Ioffe, Misha Feigel’man M. Feigel’man, et al., PRL (2007) M. Feigel’man, et al,Ann. Phys. (2010) M. Feigel’man, et al,PRB (2010) resistivity × 2 • Proliferation of incoherent –localized— Cooper-pairs when approaching the SIT

  30. Pseudogap above Tc : preformed pairs T-dependence of the local DOS Tc Pseudogap in TiN and NbN films : B. Sacépé, et al.Nature Commun. 1:140 (2010) M. Mondal, et al. PRL 106, 047001 (2011)

  31. Pseudogap in quasi-2D conventional superconductors Superconducting fluctuations in quasi-2D TiN films ( thickness < 5nm ) B. Sacépé, et al. Nature Commun.1:140 (2010) A. Varlamov and V. Dorin, Sov. Phys. JETP 57, 1089, (1983)

  32. Local versus macroscopic phase coherence BCS peaks appears at Tc independently of gap inhomogeneities Tpeak : Temperature below which peaks start to grow • BCS peaks give a local signature of the superconducting phase coherence 

  33. Condensation versus localization of preformed Cooper pairs Formation of a pseudogap without BCS peaks at T>Tc • Local pairing without phase coherence at T > Tc Preformed Cooper-pairs « Insulating » gap at T<<Tc • Local pairing without phase coherence at T << Tc Spectral signature of localized Cooper pairs

  34. Conclusions • Preformed Cooper-Pairs above Tc • Pseudogap in the DOS between Tc and ~ 3-4 Tc • “Partial” condensation of pairs below Tc • Rectangular spectra at 50mK = localized Cooper pairs • SIT occurs through the localization of Cooper pairs • Gap in the DOS remains & coherence peaks disappear Localization of preformed Cooper pairs in disordered superconductors Nature Physics 7, 239 (2011)

  35. Coulomb interaction : Zero-Bias Anomaly Disorder-enhanced Coulomb interaction B. Altshuler, et al., Phys. Rev. Lett. 44, 1288, (1980)

  36. Quantum corrections to the DOS Soft coulomb gap TiN 1 Superconducting fluctuations We need a global theory !

  37. Quantum corrections to the conductivity Superconducting fluctuations (2D Aslamasov-Larkin correction …) Disorder-enhanced Coulomb interaction (2D weak-localization/Aronov-Altshuler corrections)

  38. Dynamical Coulomb blockade P. Joyez and D. Estève,PRB 56, 1848, (1997)

  39. Magnetic field-tuned SIT Amorphous indium oxyde d = 15 nm Huge magnetoresistance peak : superconductivity-related ?

  40. Spectral fluctuations Coherence peak map Spectral gap map

  41. Disorder-induced inhomogeneities in TiN Disorder-tuned SIT in ultra-thin films of TiN Titanium nitride T. Baturina (Novosibirsk) V. Vinokur (Argonne National Lab.) Gaped insulator made of localized Cooper pairs ? B. Sacépé, et al. PRL 101, 157006 (2008)

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