Quantum-geometric thermal conductivity of superconductors

TL;DR

This paper uncovers a quantum-geometric contribution to the thermal conductivity of superconductors, linking it to the quantum metric and establishing bounds related to superfluid properties.

Contribution

It introduces a novel quantum-geometric term in thermal conductivity derived from coupling BCS theory with gravitomagnetic effects, expanding understanding of superfluid responses.

Findings

Quantum-geometric contribution governed by quantum metric.

Bounds on thermal Meissner stiffness related to superfluid weight.

Lower bound of thermal stiffness linked to Chern number.

Abstract

By coupling Bardeen-Cooper-Schrieffer (BCS) theory with isolated bands to an external gravitomagnetic vector potential via a gravitomagnetic Peierls substitution, we identify a quantum-geometric contribution to the electronic contribution of the thermal conductivity. This contribution is governed by the quantum metric in the parameter space spanned by the components of the external gravitomagnetic vector potential which corresponds to a weighted quantum metric in momentum space. In the flat-band limit, we establish an upper and lower Wiedemann-Franz-type bound for the ratio of thermal Meissner stiffness and electric Meissner stiffness (superfluid weight), whose prefactors are provided by the extrema of the squared energy offsets of the outer single-particle bands of the system. Similarly to the superfluid weight, this also leads to a lower bound of the thermal Meissner stiffness in terms of the Chern number. Our results apply to both superconductors and other fermionic superfluids.