Gaplessness from disorder and quantum geometry in gapped superconductors

Abstract

It is well known that disorder can induce low-energy Andreev bound states in a sign-changing, but fully gapped, superconductor at $\pi -$junctions. Generically, these excitations are localized. Starting from a superconductor with a sign-changing and nodeless order parameter in the clean limit, here we demonstrate a mechanism for increasing the localization length associated with the low-energy Andreev bound states at a fixed disorder strength. We find that the Fubini-Study metric associated with the electronic Bloch wavefunctions controls the localization length and the hybridization between bound states localized at distinct $\pi -$junctions. We present results for the inverse participation ratio, superfluid stiffness, site-resolved and disorder-averaged spectral functions as a function of increasing Fubini-Study metric, which indicate an increased tendency towards delocalization. The low-energy properties resemble those of a dirty nodal superconductor with gapless Bogoliubov excitations. We place these results in the context of recent experiments in moire graphene superconductors.

13 pages, 11 figures

References in corpus (56)

• Maximally-localized generalized Wannier functions for composite energy bands
• Random-Matrix Theory of Quantum Transport
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Anderson Transitions
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Magic Angle Spectroscopy
• Origin of Magic Angles in Twisted Bilayer Graphene
• Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle
• Fractional quantum Hall effect in the absence of Landau levels
• Spectroscopic signatures of many-body correlations in magic angle twisted bilayer graphene
• Superfluidity in topologically nontrivial flat bands
• Fractional Chern Insulator
• Strain Solitons and Topological Defects in Bilayer Graphene
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Fractional Quantum Hall Physics in Topological Flat Bands
• Defects in correlated metals and superconductors
• Mapping the twist angle and unconventional Landau levels in magic angle graphene
• Band geometry of fractional topological insulators
• Band geometry, Berry curvature and superfluid weight
• Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
• Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
• Geometric and conventional contribution to superfluid weight in twisted bilayer graphene
• Ferromagnetism in narrow bands of moiré superlattices
• Essay: Where Can Quantum Geometry Lead Us?
• Fragile topology and flat-band superconductivity in the strong-coupling regime
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• A Microscopic Perspective on Moiré Materials
• Heat transport as a probe of superconducting gap structure
• Andreev Bound States and Their Signatures
• Locating the missing superconducting electrons in overdoped cuprates
• Superconductivity, pseudogap, and phase separation in topological flat bands: a quantum Monte Carlo study
• Optical Spectral Weight, Phase Stiffness and Tc Bounds for Trivial and Topological Flat Band Superconductors
• Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Fluctuations, uncertainty relations, and the geometry of quantum state manifolds
• The Ginzburg-Landau theory of flat band superconductors with quantum metric
• Optical conductivity of overdoped cuprate superconductors: application to LSCO
• Heuristic bounds on superconductivity and how to exceed them
• Diamagnetic response and phase stiffness for interacting isolated narrow bands
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• Fractionalization and topology in amorphous electronic solids
• Theory of Correlated Insulators and Superconductor at $\nu =1$ in Twisted WSe${}_2$
• Anomalous Coherence Length in Superconductors with Quantum Metric
• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Phase transition beneath the superconducting dome in BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Upper bounds on superconducting and excitonic phase-stiffness for interacting isolated narrow bands
• Low-energy optical sum-rule in moiré graphene
• Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion
• Robustness of flat band superconductivity against disorder in a two-dimensional Lieb lattice model
• Intertwined Magnetism and Superconductivity in Isolated Correlated Flat Bands
• Inhomogeneity, Fluctuations, and Gap Filling in Overdoped Cuprates
• Generalized Peierls substitution for Wannier obstructions: response to disorder and interactions