Band geometry, Berry curvature and superfluid weight

TL;DR

This paper develops a theoretical framework to separate geometric and conventional contributions to superfluid weight in multiband systems, linking the geometric part to quantum metrics and Berry curvature, with applications to models relevant for ultracold atoms.

Contribution

It introduces a method to distinguish geometric superfluid weight from the conventional part, relating it to quantum metrics and Berry curvature, applicable to systems with or without time reversal symmetry.

Findings

Geometric superfluid weight is linked to quantum metric and Berry curvature.

A lower bound on superfluid weight is established based on Berry curvature.

The theory is validated against numerical methods in specific models.

Abstract

We present a theory of the superfluid weight in multiband attractive Hubbard models within the Bardeen-Cooper-Schrieffer (BCS) mean field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems with or without time reversal symmetry. In both cases the geometric superfluid weight can be related to the quantum metric of the corresponding noninteracting systems. This leads to a lower bound on the superfluid weight given by the absolute value of the Berry curvature. We apply our theory to the attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can be realized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results.