Geometric origin of superfluidity in the Lieb lattice flat band

TL;DR

This paper reveals that superfluidity in the Lieb lattice flat band arises from geometric properties of the band structure, linking superfluid weight to the quantum metric and interaction strength, with implications for high-Tc superconductors.

Contribution

It demonstrates that superfluid weight in a flat band is governed by geometric band structure invariants, providing a new understanding of superfluidity in flat band systems.

Findings

Superfluid weight can be large even in an isolated flat band.

Superfluid weight is proportional to interaction strength and quantum metric.

Predictions are testable with ultracold gases and relate to high-Tc superconductors.

Abstract

The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure invariant obtained from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.