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Disorder and Zeeman Field-driven superconductor-insulator transition

Nandini Trivedi The Ohio State University. Disorder and Zeeman Field-driven superconductor-insulator transition. Mohit Randeria. Yen Lee Loh. Karim Bouadim. See Poster. “Exotic Insulating States of Matter”, Johns Hopkins University, Jan 14-16, 2010. SC. I. *. disorder.

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Disorder and Zeeman Field-driven superconductor-insulator transition

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  1. Nandini Trivedi The Ohio State University Disorder and Zeeman Field-driven superconductor-insulator transition Mohit Randeria Yen Lee Loh Karim Bouadim See Poster “Exotic Insulating States of Matter”, Johns Hopkins University, Jan 14-16, 2010

  2. SC I * disorder SUPERCONDUCTOR-INSULATOR TRANSITION QPT amorphous quench condensed films T I “disorder” What kind of insulator? Exotic? Unusual? Trivial? Band? Anderson? Mott? Wigner? Topological? Quantum Hall? Bose Glass? Fermi glass? Vortex glass? SC Haviland et.al. PRL 62, 2180 (’89) Valles et.al. PRL 69, 3567 (’92) Hebard in “Strongly Correlated Electronic Systems”, ed. Bedell et. al. (’94) Goldman and Markovic, Phys. Today 51, 39 (1998)

  3. Outline of talk: • Focus on three puzzling pieces of data: • Adams: Origin of low energy states in tunneling • DOS in field-tuned SIT • Sacépé: Disappearance of coherence peaks • in density of states above Tc • Armitage: Origin of states within the SC gap • observed in

  4. P(V) -V 0 V Model: Attractive Hubbard + disorder + field Kinetic energy 2D + Attraction (U controls size of Cooper pairs) + Random potential Zeeman Field V=0 s-wave SC |U|=0 localization problem of non-interacting electrons * Ignore Coulomb interactions

  5. Methods Bogoliubov-de Gennes-Hartree-Fock MFT • Local expectation values • Solve self consistently BdG keeps only amplitude fluctuations Determinantal Quantum Monte Carlo No sign problem for any filling Keeps both amplitude and phase fluctuations Maximum entropy method for analytic continuation DOS and LDOS

  6. Part I: Superconducting Film in Zeeman Field:Soft Gaps in DOS Where do the states at zero bias come from? Magnetic impurities? Orbital pair breaking? ?? states in gap Experiment Tunneling conductance into exchange-biased superconducting Al films Catelani, Xiong, Wu, and Adams, PRB 80, 054512 (2009)‏ Also Adams, private communication

  7. Part I: Superconducting Film in Zeeman Field:Soft Gaps in DOS states in gap Theory Disordered LO states provide spectral signatures at low energy Loh and Trivedi, preprint Experiment Tunneling conductance into exchange-biased superconducting Al films Catelani, Xiong, Wu, and Adams, PRB 80, 054512 (2009)‏

  8. SC + Zeeman field ↑ ↓ ↑ k −k BCS FL pairing Δ Δ0 polarization m Zeeman field h Chandrasekhar, Appl. Phys. Lett., 1, 7 (1962); Clogston, PRL 9, 266 (1962)‏

  9. Modulated (LO) SC order parameter m m Δ Δ Δ m x Δ m Weak LO FL BCS Strong LO Microscale phase separation = polarized domain walls pairingΔ Δ0 polarization m h hc2 hc hc1 Y-L. Loh and Trivedi, arxiv 0907.0679

  10. Disorder + Zeeman field h = 0.8 Local magnetization Spin resolved DOS Local Pairing amplitude DOS I. Paired unpolarized SC In the next slide Put a title sort of zeeman + disorder Remove the h=1.75 panel Give color bars in each case plot the total dos And most importantly Have each set of panels for a given h come on In a timed way at the push of “enter”

  11. Disorder + Zeeman field h = 0.95 + and − domains soft gap Disordered LO

  12. m>0.05 F>0.05 F<−0.05 magnetization in domain walls + pairing - pairing Close-up view of a disordered LO state (h=1)‏

  13. Disorder + Zeeman field h = 1.5 + and − domains Non-superconducting

  14. Spectrum Magnetization Pairing hard gap BCS + and - domains Disordered LO soft gap gapless Normalstate

  15. Part II: Local and Total Density of States

  16. Previous Results:Self consistent mean field theory Bogoliubov de-Gennes (BdG) T=0 Pairing amplitude DOS Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)

  17. Previous Results:Self consistent mean field theory Bogoliubov de-Gennes (BdG) Gap in single particle DOS persists in insulator Pairing amplitude DOS T=0 GAP Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)

  18. Why is the gap finite? Where do excitations live? high hills: empty D~0 D~0 Pairing amplitude map D(r) deep valleys: trapped pairs no number fluctuations SC islands formed where |V(r)-m| is small Lowest excited states live on SC blobs Lowest excited states GAP PERSISTS Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002)

  19. What happens when phase fluctuations are included?

  20. Phase Diagram U=-4t n=0.88 Pairing scale N PG (generated by disorder) Coherence scale INS SC

  21. Determining T*: peak in spin susceptibility N T T* SC INS Disorder

  22. Determining Tc: Vanishing of Superfluid stiffness N T T* Tc SC INS Disorder Twisted Boundary Condition

  23. Spectral properties

  24. N 0.33 0.2 T SC INS 0 1.6 Disorder

  25. N 0.33 0.2 T SC INS 0 1.6 Disorder

  26. N 0.33 0.2 T SC INS 0 1.6 Disorder

  27. N 0.33 0.2 T SC INS 0 1.6 Disorder

  28. QMC DOS for SC: T dependence N U=-4t V=1 Gapless 0.33 PG T*(QMC) ~ 0.6 0.2 T SC Pseudogap Coh peaks destroyed INS 0 1.6 Disorder T < Tc T = Tc Tc(QMC) ~ 0.12 SC gap Coh peaks T > Tc 28 Improve Schematic With less jaggedy curve for SC Indicate U, Vc, Tc(V=0)_QMC and T*(V=0) QMC on the schematic fig Δ < Eg Δ0/Tc < 1.84

  29. Temperature Dependence of DOS Experiments: Scanning tunneling spectroscopy(B. Sacépé et al.)‏ Theory:Bogoliubov-de Gennes-Hartree-Fock, determinant quantum Monte Carlo 29

  30. QMC DOS: V dependence N U=-4t T=0.1 Ins gap No coh peaks 0.33 0.2 Vc~1.6t T SC INS 0 1.6 Disorder BdG gap SC gap Coh peaks

  31. DOS: Summary T T T N N N INS SC INS SC INS SC V V V INS gap closes No coh peaks SC gap closes Coh peaks die Gap survives Coh peaks die

  32. Local Density of States

  33. yes, we DO understand the weird behavior Site (5, 4)‏ Pairing survives with V Site (5, 1)‏ Pairing destroyed by V Coherence peak destroyed; incoherent weight builds up Coherence peak survives 33

  34. Local DOS: T dependence Pairing FBdG(r, T) disappears at every site at the same temperature, T=TBdG. “Coherence peaks” in LDOS NQMC(r, ω, T) disappear at every site at the same T ~ Tc. Pseudogap remains on every site up to T*.

  35. Local DOS: T dependence c.f. Experiment (Sacépé): Scanning tunneling spectroscopy on an amorphous InOx film (thickness 15 nm, on Si/SiO2 substrate)with Tc ~ 1.7 K, at two different locations at various T “Coherence peaks” disappear at every site at the same temperature Pseudogaps still exist above Tc 35 More details about expt: are these at two different sites; What is the Tc of these films; other exptl details;

  36. Main Results: 1. Disordered LO states provide spectral signatures at low energy for Zeeman-field tuned superconductors 2. Coherence peaks disappear at every site at the same T~Tc Pseudogaps disappear at every site at T ~ T* In disorder tuned transition the gap survives BUT coherence peaks die at V~Vc

  37. Paired Insulator Phase disordered Disorder

  38. The End

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