Interplay of local and global quantum geometry in the stability of flat-band superfluids

TL;DR

This paper explores how quantum geometry influences flat-band superfluidity, revealing that superfluid stability depends on the distribution of quantum metric across the Brillouin zone and requires at least three bands in 2D systems.

Contribution

It demonstrates the significant role of quantum geometry in flat-band superfluidity and establishes conditions for its stability, including the necessity of multiple bands.

Findings

Superfluid weight has a contribution proportional to the condensate quantum metric.

Stable flat-band superfluidity in 2D requires at least three bands.

Distribution of quantum metric in the Brillouin zone is crucial for superfluidity.

Abstract

Quantum geometry strongly impacts physical properties in flat-band systems. We consider its role in bosonic condensation and superfluidity on flat bands, and show that the superfluid weight has an important contribution proportional to the condensate quantum metric. Based on this result, we uncover conditions under which flat-band superfluidity is unlikely. For instance, we find that stable flat-band superfluidity in a two-dimensional system requires at least three bands within Bogoliubov theory. Because the quantum geometry at the condensation momentum plays a disproportionately large role, a large integrated quantum metric is not sufficient for flat-band superfluidity, but how the quantum metric is distributed in the Brillouin zone is crucial.