# Superfluid stiffness for the attractive Hubbard model on a honeycomb optical lattice

## TL;DR

This paper investigates the superfluid phase stiffness in a two-component Fermi gas on a honeycomb lattice, highlighting both conventional and geometric contributions, and maps out phase diagrams for the critical transition temperature.

## Contribution

It introduces a comprehensive theoretical framework that includes geometric effects via the quantum metric in superfluid stiffness calculations for the honeycomb lattice.

## Key findings

- Both conventional and geometric contributions significantly influence superfluid stiffness.
- Phase diagrams show how critical temperature varies with chemical potential, filling, interaction, and hopping.
- The approach combines BCS mean-field theory with the BKT relation for phase fluctuations.

## Abstract

In addition to the conventional contribution that is directly controlled by the single-particle energy spectrum, the superfluid phase stiffness of a two-component Fermi gas has a geometric contribution that is governed by the quantum metric of the honeycomb's band structure. Here, we take both contributions into account, and construct phase diagrams for the critical superfluid transition temperature as a function of the chemical potential, particle filling, onsite interaction and next-nearest-neighbor hopping. Our theoretical approach is based on a self-consistent solution of the BCS mean-field theory for the stationary Cooper pairs and the universal BKT relation for the phase fluctuations.