Geometric and conventional contributions to superfluid weight in the minimal models for superconducting copper-doped lead apatite

TL;DR

This study investigates the geometric and conventional factors influencing superfluid weight in minimal models of copper-doped lead apatite, revealing that superfluid weight can vary significantly depending on magnetic phases and band topology.

Contribution

The paper introduces a theoretical framework for the geometric contribution to superfluid weight in flat bands, highlighting differences between ferromagnetic and paramagnetic phases.

Findings

Superfluid weight has no lower bound in these models.

Superfluid weight varies greatly with model parameters in ferromagnetic phases.

In paramagnetic phases, superfluid weight remains large and geometrically significant.

Abstract

The density functional theory calculations and tight-binding models for the copper-doped lead apatite support flat bands, which could be susceptible to the emergence of high-temperature superconductivity. We develop theory for the geometric contribution of the superfluid weight arising from the momentum-space topology of the Bloch wave functions of these flat bands, and we compare our results to the paradigmatic case of $s$-wave superconductivity on an isolated topological flat band. We show that, in contrast to the standard paradigm of flat-band superconductivity, there does not exist any lower bound for the superfluid weight in these models. Moreover, although the nontrivial quantum geometries of the normal state bands are the same when the superconductivity appears in the ferromagnetic and paramagnetic phases, the emerging superconducting phases have very different superfluid weights. In the case of superconductivity appearing on the spin-polarized bands the superfluid weight varies a lot as a function of model parameters. On the other hand, if the superconductivity emerges in the paramagnetic phase the superfluid weight is robustly large and it contains a significant geometric component.