Fractal superconductivity near localization threshold

Abstract

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy $E_F$ is located in the region of localized states not so far from the Anderson mobility edge $E_c$. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model. Our theoretical analysis is based on the analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems. We identify three distinct phases: 'critical' superconductive state formed at $E_F=E_c$, superconducting state with a strong pseudogap, realized due to pairing of weakly localized electrons and insulating state realized at $E_F$ still deeper inside localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gaped state is the presence of two independent energy scales: superconducting gap $\Delta$, that is due to many-body correlations and a new "pseudogap" energy scale ${\Delta }_P$ which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive $T_c$. Two gap nature of the "pseudo-gaped superconductor" is shown to lead to a number of unusual physical properties.

110 pages, 39 figures. The revised version corrects a number of typos, adds references and discussion of recent results

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Cited by in corpus (156)

• Localization of preformed Cooper-pairs in disordered superconductors
• Coherent quantum phase slip
• Phase fluctuations in a strongly disordered s-wave superconductor close to the metal-insulator transition
• Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon
• Quantum breakdown of superconductivity in low-dimensional materials
• Phase diagram of a strongly disordered s-wave superconductor, NbN, close to the metal-insulator transition
• Enhancement of superconductivity by Anderson localization
• Disorder induced multifractal superconductivity in monolayer niobium dichalcogenides
• Statistics of eigenstates near the localization transition on random regular graphs
• Evidence for a Finite Temperature Insulator
• Superconductor-Insulator transition and energy localization
• A disorder-enhanced quasi-one-dimensional superconductor
• Universal scaling of the order-parameter distribution in strongly disordered superconductors
• Enhancing Superconductivity by Disorder
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Conventional superconductivity in quasicrystals
• Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
• Superconductivity of disordered Dirac fermions
• Collective energy gap of preformed Cooper-pairs in disordered superconductors
• Effective medium theory for superconducting layers: A systematic analysis including space correlation effects
• Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs
• Superfluid density and phase relaxation in superconductors with strong disorder
• Confinement of superconducting fluctuations due to emergent electronic inhomogeneities
• Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?
• Spectroscopic evidence for strong correlations between local superconducting gap and local Altshuler-Aronov density-of-states suppression in ultrathin NbN films
• Multifractality at Anderson transitions with Coulomb interaction
• Superconductor-insulator transitions: Phase diagram and magnetoresistance
• Anomalous gap edge dissipation in disordered superconductors on the brink of localization
• Universal Broadening of the Bardeen-Cooper-Schrieffer Coherence Peak of Disordered Superconducting Films
• Global critical temperature in inhomogeneous superconductors induced by multifractality
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
• Superconductivity, charge- or spin-density wave, and metal-nonmetal transition in BaTi${}_2$(Sb${}_{1-x}$Bi${}_x$)${}_2$O
• Direct observation of the superconducting gap in thin film of titanium nitride using terahertz spectroscopy
• Anomalous metallic state above the upper critical field of the conventional three-dimensional superconductor AgSnSe2 with strong intrinsic disorder
• Enhanced, phase coherent, multifractal-like, two-dimensional superconductivity
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• Superconductivity of disordered Dirac fermions in graphene
• On the application of Mattis-Bardeen theory in strongly disordered superconductors
• Berezinskii-Kosterlitz-Thouless transition in homogeneously disordered superconducting films
• Emergence of Quantum Phase-Slip Behaviour in Superconducting NbN Nanowires: DC Electrical Transport and Fabrication Technologies
• High field termination of a Cooper-pair insulator
• Kondo-Anderson Transitions
• Direct Observation of Fragmentation in a Disordered, Strongly Interacting Fermi Gas
• Return probability and scaling exponents in the critical random matrix ensemble
• Collapse of the Cooper pair phase coherence length at a superconductor to insulator transition
• Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor
• Superconductivity at the three-dimensional Anderson metal-insulator transition
• Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals
• Systematic investigation of the effects of disorder at the lowest order throughout the BCS-BEC crossover
• Superconductor-Insulator Transition in disordered Josephson junction chains
• Multifractally-enhanced superconductivity in thin films
• Quantum meets classical phase transition: Low-temperature anomaly in disordered superconductors near $B_{c2}$
• Enhancement of critical temperatures in disordered bipartite lattices
• Glassy properties of Anderson localization: pinning, avalanches and chaos
• Effect of annealing on the superconducting properties of a-Nb(x)Si(1-x) thin films
• Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems
• Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys under pressure
• Microwave properties of superconductors close to SIT
• Enhanced Superconductivity in Quasi-periodic Crystals
• Josephson effect in a Fibonacci quasicrystal
• Amplitude, density and current correlations of strongly disordered superconductors
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Self-consistent-field ensembles of disordered Hamiltonians: Efficient solver and application to superconducting films
• Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors
• Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets
• Enhanced Amplitude for Superconductivity due to Spectrum-wide Wave Function Criticality in Quasiperiodic and Power-law Random Hopping Models
• Incorporating Dynamic Mean-Field Theory into Diagrammatic Monte Carlo
• Localization of disordered bosons and magnets in random fields
• Mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction
• Thermally activated conductance in arrays of small Josephson junctions
• Strong Suppression of Coherence Effect and Appearance of Pseudogap in Layered Nitride Superconductor Li_xZrNCl: ^91Zr- and ^15N- NMR Studies
• Quasidisorder Induced Topology
• Strong quantum interference in strongly disordered bosonic insulators
• Generalized multifractality at spin quantum Hall transition
• Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator Transition
• Visualizing the multifractal wavefunctions of a disordered two-dimensional electron gas
• Enhanced quantum metric due to vacancies in graphene
• Quasi-1-Dimensional Superconductivity in Highly Disordered NbN Nanowires
• Pseudogap and weak multifractality in disordered Mott charge-density-wave insulator
• Self- and Mutual Inductance of NbN and Bilayer NbN/Nb Inductors in Planarized Fabrication Process With Nb Ground Planes
• Superconductivity suppression in disordered films: Interplay of two-dimensional diffusion and three-dimensional ballistics
• Magnetic field induced transition from a vortex liquid to Bose metal in ultrathin a-MoGe thin film
• Multifractally-enhanced superconductivity in two-dimensional systems with spin-orbit coupling
• Excessive Noise as a Test for Many-Body Localization
• Dielectric response of Anderson and pseudogapped insulators
• Ferromagnetism in a Repulsive Atomic Fermi Gas with Correlated Disorder
• Characterizing dielectric properties of ultra-thin films using superconducting coplanar microwave resonators
• Interplay of superconductivity and localization near a 2D ferromagnetic quantum critical point
• Two-component Coulomb Glass in Disordered Superconducting Films
• Overactivated transport in the localized phase of the superconductor-insulator transition
• Droplets of the order parameter in a low density attracting electron system in the presence of a strong random potential
• Amplitude Fluctuations Driven by the Density of Electron Pairs within Nanosize Granular Structuters inside Strongly Disordered Superconductors: Evidence for a Shell-Like Effect
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Generalized surface multifractality in 2D disordered systems
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Near-power-law temperature dependence of the superfluid stiffness in strongly disordered superconductors
• Scale-dependent theory of the disordered electron liquid
• Superconductivity in a disordered metal with Coulomb interactions
• Hartree-Fock study of an Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents
• Origin of Topological Order in a Cooper Pair Insulator
• Ultrasonic attenuation in a pseudogapped superconductor
• Local density of state fluctuations in 2D superconductor as a probe of quantum diffusion
• Fractal Nodal Band Structures
• Emergent multifractality in power-law decaying eigenstates
• Instability of insulators near quantum phase transitions
• Electron-phonon cooling power in Anderson insulators
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Josephson effect in a fractal geometry
• Strange metal state near quantum superconductor-metal transition in thin films
• Magnetic disorder in superconductors: Enhancement by mesoscopic fluctuations
• Quasiparticle Screening near a Bosonic Superconductor-Insulator Transition Revealed by Magnetic Impurity Doping
• Modeling and simulations of quantum phase slips in ultrathin superconducting wires
• Enhancement of Superconductivity in a Dirty Marginal Fermi Liquid
• The Temperature dependence of the magneto-resistance peak in highly disordered superconductors
• Little-Parks Oscillations in a Single Ring in the vicinity of the Superconductor-Insulator Transition
• Beta-functions of non-linear $\sigma$-models for disordered and interacting electron systems
• Low-energy dynamical response of an Anderson insulator with local attraction
• Paraconductivity of pseudogapped superconductors
• Mean-field theory of first-order quantum superconductor-insulator transition
• Effect of the Anomalous Diffusion of Fluctuating Cooper Pairs in the Density of States of Superconducting NbN Thin Films
• Fluctuation-induced odd-frequency spin-triplet pairing in disordered electron liquid
• Superfluid transition in disordered dipolar Fermi gases
• Two-dimensional Coulomb glass as a model for vortex pinning in superconducting films
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Distribution of the order parameter in strongly disordered superconductors: An analytic theory
• Quasiperiodicity-induced enhancement of superconductivity in one-dimensional critical systems
• Boundary multifractality in the spin quantum Hall symmetry class with interaction
• Quantum Fluctuations and Multifractally-Enhanced Superconductivity in Disordered Thin Films
• Refined cyclic renormalization group in Russian Doll model
• Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene
• Universally enhanced superconductivity and coexisting ferroelectricity at oxide interfaces
• Pressure tuning of localization and superconductivity in LaOPbBiS${}_3$ and La${}_2$O${}_2$Bi${}_3$AgS${}_6$
• Two-Dimensional Phase-Fluctuating Superconductivity in Bulk-Crystalline NdO${}_{0.5}$F${}_{0.5}$BiS${}_2$
• Cooper Pair Insulator phase induced in amorphous Pb${}_0.9$Bi${}_0.1$ thin films
• Critical anomalous metals near superconductivity in models with random interactions
• Strong phase coherence and vortex matter in a fractal system with proximity-induced superconductivity
• Non-equilibrium restoration of duality symmetry in the vicinity of the superconductor-insulator transition
• Distribution of critical temperature at Anderson localization
• Model-independent determination of the gap function of nearly localized superconductors
• Partial Decoherence and Thermalization through Time-Domain Ergodicity
• Holographic nature of critical quantum states of proteins
• Direct observation of intrinsic surface magnetic disorder in amorphous superconducting films
• Advanced approach of superconducting gap function extraction from tunneling experiments
• Superfluid transition in quasi-two-dimensional disordered dipolar Fermi gases
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe
• Magnetic instability and spin-glass order beyond the Anderson-Mott transition in interacting power-law random banded matrix fermions
• Enhancing long-range order in disordered two-band s-wave superconductors
• Universal fluctuations of localized two interacting particles in one dimension
• 2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes
• Universal Relation between Spectral and Wavefunction Properties at Criticality
• Reduction of electron repulsion and enhancement of $T_c$ in small diffusive superconducting grains
• Establishment of global phase coherence in a highly disordered fractal MgO/MgB2 nanocomposite: Roles of interface, morphology and defect
• Spatial homogeneity of superconducting order parameter in NbN films grown by atomic layer deposition
• Spectroscopic evidence of disorder-induced quantum phase transitions in monolayer Fe(Te,Se) superconductor
• Multifractal correlations of the local density of states in dirty superconducting films