Quantum geometric origin of the Meissner effect and superfluid weight marker

TL;DR

This paper reveals that the superfluid weight and Meissner effect in superconductors originate from the quantum metric in momentum space, linking geometric properties to superconducting stability and response.

Contribution

It introduces a formalism connecting quantum metric to superfluid weight in multiband superconductors, enabling disorder effects to be incorporated via Bogoliubov-de Gennes equations.

Findings

Quantum metric determines superfluid weight in superconductors.

Disorder induces turbulence in diamagnetic currents.

London penetration depth increases with disorder, matching experiments.

Abstract

The momentum space of conventional superconductors is recently recognized to possess a quantum metric defined from the overlap of filled quasihole states at neighboring momenta. For multiband superconductors with arbitrary intraband and interband s-wave pairing, we elaborate that their superfluid weight in London equations is given by the momentum integration of the elements of quantum metric times the quasiparticle energy, indicating the quantum geometric origins of Meissner effect and vortex state. The momentum integration of the quantum metric further yields a spread of quasihole Wannier functions that characterizes the stability of the superconducting state. Our formalism allows the diamagnetic response of conventional superconductors to be mapped to individual lattice sites as a superfluid weight marker, which can incorporate the effect of disorder through self-consistently solving the Bogoliubov-de Gennes equations. Using single-band s-wave superconductors in 2D and 3D as examples, our marker reveals a diamagnetic current that becomes turbulent in the presence of nonmagnetic impurities, and the increase of London penetration depth by disorder that is consistent with experiments.