Geometric superfluid weight of composite bands in multiorbital superconductors

TL;DR

This paper develops a perturbation method to analyze the superfluid weight in multiorbital superconductors, revealing how lattice geometry and quantum metrics influence superfluid properties in composite flat bands.

Contribution

It introduces a perturbation approach to study superfluid weight in composite bands, including inter-band effects and a topological lower bound, with an analytical formula for lattice geometric contributions.

Findings

Derived an analytical expression for lattice geometric contribution to superfluid weight.

Identified a topological lower bound for superfluid weight in flat band composites.

Provided a practical formula for calculating superfluid weight using Bloch functions.

Abstract

The superfluid weight of an isolated flat band in multi-orbital superconductors contains contributions from the band's quantum metric and a lattice geometric term that depends on the orbital positions in the lattice. Since the superfluid weight is a measure of the superconductor's energy fluctuation, it is independent of the lattice geometry, leading to the minimal quantum metric of a band [Phys. Rev. B 106, 014518 (2022)]. Here, a perturbation approach is developed to study the superfluid weight and its lattice geometric dependence for composite bands. When all orbitals exhibit uniform pairing, the quantum geometric term contains each band's contribution and an inter-band contribution between every pair of bands in the composite. Based on a band representation analysis, they provide a topological lower bound for the superfluid weight of an isolated composite of flat bands. Using this perturbation approach, an analytical expression of the lattice geometric contribution is obtained. It is expressed in terms of Bloch functions, providing a convenient formula to calculate the superfluid weight for multi-orbital superconductors.