Flat-band ratio and quantum metric in the superconductivity of modified Lieb lattices

TL;DR

This study investigates how relaxing common assumptions affects flat band superconductivity in Lieb lattices, highlighting the roles of quantum geometry and flat-band ratio in determining critical temperatures.

Contribution

It extends previous theories by analyzing superconductivity in non-ideal conditions using dynamical mean-field theory on modified Lieb lattices.

Findings

Flat-band ratio and quantum geometry are good indicators of superconductivity at finite temperatures.

Superfluid weight and flat-band ratio guide the BKT temperature in non-isolated flat bands.

Superconducting properties depend on band isolation and lattice modifications.

Abstract

Flat bands may offer a route to high critical temperatures of superconductivity. It has been predicted that the quantum geometry of the bands as well as the ratio of the number of flat bands to the number of orbitals determine flat band superconductivity. However, such results have assumed at least one of the following: an isolated flat band, zero temperature, mean-field theory, and/or uniform pairing. Here, we explore flat band superconductivity when these assumptions are relaxed. We consider an attractive Hubbard model for different extensions of the Lieb lattice. The superconducting order parameter, critical temperature, superfluid weight, and Berezinskii-Kosterlitz-Thouless (BKT) temperature are calculated within dynamical mean-field theory. We find that for isolated flat bands, the flat-band ratio and quantum geometry are in general good indicators of superconductivity even at finite temperatures. For non-isolated flat bands, a good guideline of the BKT temperature is provided by the zero-temperature superfluid weight and the flat-band ratio.