Superfluid weight in disordered flat-band superconductors as a competition between localization functionals

Abstract

According to Anderson's theorem, the gap of a time-reversal symmetric weak-coupling superconductor is unaffected by non-magnetic disorder. However, the superfluid weight (stiffness) is reduced in the disordered limit by a factor of $\Delta \tau$, a product of the scattering time $\tau$ and the superconducting order parameter $\Delta$. Here we show that the opposite holds true in flat-band superconductors. While non-magnetic disorder does reduce the order parameter, we find that its direct effect on superfluid weight is mostly negligible. We show analytically that the effect of disorder is to lowest order given in terms of the difference between the intraband and interband parts of the localization functional of impurity wavefunctions, finding it to be typically vanishing.

5 pages + Supplementary. Published version

References in corpus (27)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Maximally-localized generalized Wannier functions for composite energy bands
• Maximally localized Wannier functions: Theory and applications
• Superfluidity in topologically nontrivial flat bands
• Moiré heterostructures as a condensed matter quantum simulator
• Artificial flat band systems: from lattice models to experiments
• Superconductivity in rhombohedral trilayer graphene
• Geometric origin of superfluidity in the Lieb lattice flat band
• Superfluidity and Quantum Geometry in Twisted Multilayer Systems
• Band geometry of fractional topological insulators
• Role of Spatial Amplitude Fluctuations in Highly Disordered s-Wave Superconductors
• Band geometry, Berry curvature and superfluid weight
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Quantum metric and effective mass of a two-body bound state in a flat band
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Preformed pairs in flat Bloch bands
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Superconducing Alloys with Weak and Strong Scattering: Anderson's Theorem and a Superconductor-Insulator Transition
• Superfluid weight in the isolated band limit within the generalized random phase approximation
• Metal-insulator transition in infinitesimally weakly disordered flatbands
• Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion
• Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands
• Superconductivity, generalized random phase approximation and linear scaling methods
• Robustness of flat band superconductivity against disorder in a two-dimensional Lieb lattice model
• Quantum geometry induced microwave enhancement of flat band superconductivity