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

2. SC I “disorder” * SC I disorder amorphous quench condensed films 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) SUPERCONDUCTOR-INSULATOR TRANSITION What kind of insulator? Exotic? Unusual? Trivial? Band? Anderson? Mott? Wigner? Topological? Quantum Hall? Bose Glass?Fermi glass? Vortex glass? QPT T

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. Kinetic energy + Attraction + ( U controls size of Cooper pairs) Random potential P(V) -V0V V=0 s-wave SC |U|=0 localization problem of non-interacting electrons * Ignore Coulomb interactions Zeeman Field Model: Attractive Hubbard + disorder + field 2D

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

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

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

8. 8 FL BCS h polarization m Δ0Δ0 pairing Δ k −k ↑ ↑ ↓ SC + Zeeman field Zeeman field Chandrasekhar, Appl. Phys. Lett., 1, 7 (1962); Clogston, PRL 9, 266 (1962)‏

9. 9 FL BCS Weak LO Strong LO Δ m Δ m Δ m x Δ m Modulated (LO) SC order parameter hchc h Δ0Δ0 h c1 h c2 polarization m pairing Δ Microscale phase separation = polarized domain walls Y-L. Loh and Trivedi, arxiv 0907.0679

10. h = 0.8 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” I. Paired unpolarized SC Local magnetization Local Pairing amplitude Spin resolved DOS DOS Disorder + Zeeman field

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

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

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

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

15. Part II: Local and Total Density of States

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

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

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

19. What happens when phase fluctuations are included?

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

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

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

23. Spectral properties

24. T Disorder SC N INS 0 1.6 0.2 0.33

25. T Disorder SC N INS 0 1.6 0.2 0.33

26. T Disorder SC N INS 0 1.6 0.2 0.33

27. T Disorder N INS 0 1.6 0.2 0.33 SC

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

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

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

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

32. Local Density of States

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

34. 34 Local DOS: T dependence Pairing F BdG (r, T) disappears at every site at the same temperature, T=T BdG. “Coherence peaks” in LDOS N QMC (r, ω, T) disappear at every site at the same T ~ T c. Pseudogap remains on every site up to T*.

35. 35 c.f. Experiment (Sacépé): Scanning tunneling spectroscopy on an amorphous InO x film (thickness 15 nm, on Si/SiO 2 substrate) with T c ~ 1.7 K, at two different locations at various T Local DOS: T dependence “Coherence peaks” disappear at every site at the same temperature Pseudogaps still exist above T c 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 In disorder tuned transition the gap survives BUT coherence peaks die at V~Vc 2. Coherence peaks disappear at every site at the same T~Tc Pseudogaps disappear at every site at T ~ T*

37. Disorder Paired Insulator Phase disordered

38. 38 The End