Disorder and Zeeman Field-driven superconductor-insulator transition Nandini Trivedi The Ohio State University Karim Bouadim Yen Lee Loh Mohit Randeria See Poster “Exotic Insulating States of Matter”, Johns Hopkins University, Jan 14-16, 2010 1 SUPERCONDUCTOR-INSULATOR TRANSITION amorphous quench condensed films QPT T * I I disorder What kind of insulator? Exotic? Unusual? Trivial? Band? Anderson? Mott? Wigner? Topological? Quantum Hall? Bose Glass? Fermi glass? Vortex glass? “disorder” SC 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) Outline of talk: Focus on three puzzling pieces of data: Adams: Origin of low energy states in tunneling DOS in h field-tuned SIT || Sacépé: Disappearance of coherence peaks in density of states above Tc Armitage: Origin of states within the SC gap observed in Re() Model: Attractive Hubbard + disorder + field H Kinetic energy ci c j h.c. 2D i , j + Attraction (U controls size of Cooper pairs) P(V) t + Random potential -V 0 V |U | nini i (Vi h )ni i Zeeman Field V=0 s-wave SC |U|=0 localization problem of non-interacting electrons * Ignore Coulomb interactions Methods Bogoliubov-de Gennes-Hartree-Fock MFT Local expectation values Solve self consistently n (r) c r c r (r) |U | c r c r |U | F(r) 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 1 N ( ) A(k , ) N k e G(k , ) Tck ( )c (0) d A(k , ) 1 e 5 DOS and LDOS k 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 Experiment in gap Tunneling conductance into exchange-biased superconducting Al films Catelani, Xiong, Wu, and Adams, PRB 80, 054512 (2009) Also Adams, private communication 6 Part I: Superconducting Film in Zeeman Field: Soft Gaps in DOS N(E) states Experiment in gap Tunneling conductance into exchange-biased superconducting Al films Catelani, Xiong, Wu, and Adams, PRB 80, 054512 (2009) Theory Disordered LO states provide spectral signatures at low energy Loh and Trivedi, preprint 7 SC + Zeeman field −k ↑↑ ↓ k BCS FL Δ0 pairing Δ polarization m 1 hc 0 0.707 0 2 h Zeeman field Chandrasekhar, Appl. Phys. Lett., 1, 7 (1962); Clogston, PRL 9, 266 (1962) 8 Modulated (LO) SC order parameter Δ m Δ m BCS Δ0 pairing Δ Strong LO Δ Weak LO x FL Microscale phase separation = polarized domain walls polarization m hc1 Y-L. Loh and Trivedi, arxiv 0907.0679 m m Δ hc hc2 h 9 V 2t U 4t Disorder + Zeeman field Local magnetization h = 0.8 Spin resolved DOS N ( ) Local Pairing amplitude N() DOS I. Paired unpolarized SC V 2t U 4t Disorder + Zeeman field h = 0.95 N ( ) N() + and − domains Disordered LO soft gap V 2t + pairing pairing m>0.05 F>0.05 F<−0.05 magnetization in domain walls Close-up view of a disordered LO state (h=1) 12 Disorder + Zeeman field V 2t h = 1.5 N ( ) + and − domains N() Non-superconducting Magnetization Pairing Spectrum N ( ) hard gap BCS + and domains Disordered LO N() soft gap gapless Normal state 14 Part II: Local and Total Density of States Previous Results:Self consistent mean field theory Bogoliubov de-Gennes (BdG) T=0 Pairing amplitude n (r) c r c r (r) |U | c r c r |U | F(r) Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002) DOS Previous Results:Self consistent mean field theory Gap in single particle DOS persists in insulator Bogoliubov de-Gennes (BdG) Pairing amplitude T=0 GAP S n (r) c r c r (r) |U | c r c r |U | F(r) Ghosal, Randeria, Trivedi PRL 81, 3940 (1998); PRB 65, 14501 (2002) DOS Why is the gap finite? Where do excitations live? Lowest excited states Pairing amplitude map (r) ~0 ~0 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) What happens when phase fluctuations are included? Phase Diagram U=-4t n=0.88 Pairing scale N PG (generated by disorder) SC Coherence scale INS Determining T*: peak in spin susceptibility N T* T SC INS Disorder V 21 Determining Tc: Vanishing of Superfluid stiffness N S T* T SC Tc INS Disorder V S Twisted Boundary Condition 1 E s ( )2 2 22 Spectral properties N 0.33 0.2 T SC 0 INS 1.6V Disorder N 0.33 0.2 T SC 0 INS 1.6V Disorder N 0.33 0.2 T SC 0 INS 1.6V Disorder N 0.33 0.2 T INS SC 0 1.6V Disorder QMC DOS for SC: T dependence U=-4t V=1 Gapless N 0.33 PG T*(QMC) ~ 0.6 0.2 T SC 0 Disorder INS 1.6 Pseudogap Coh peaks destroyed V T < Tc T = Tc T > Tc Tc(QMC) ~ 0.12 SC gap Coh peaks 28 Temperature Dependence of DOS Experiments: Scanning tunneling spectroscopy (B. Sacépé et al.) Theory: Bogoliubov-de Gennes-Hartree-Fock, determinant quantum Monte Carlo 29 QMC DOS: V dependence U=-4t T=0.1 N 0.33 Ins gap No coh peaks 0.2 T SC 0 Disorder INS 1.6 Vc~1.6t V BdG gap V 0 E gap,QMC ~ 0.7t SC gap Coh peaks E gap,BdG ~ 1.4t 30 DOS: Summary T T N SC N N INS V Gap survives Coh peaks die SC T SC INS INS V V SC gap closes Coh peaks die INS gap closes31 No coh peaks Local Density of States Site (5, 4) Pairing survives with V Coherence peak survives Site (5, 1) Pairing destroyed by V Coherence peak destroyed; incoherent weight builds up 33 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*. 34 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 Main Results: 1. Disordered LO states provide spectral signatures at low energy for Zeemanfield 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 Disorder Paired Insulator Phase disordered The End 38