# Origin of flat-band superfluidity on the Mielke checkerboard lattice

## TL;DR

This paper investigates the quantum-geometric origins of flat-band superfluidity in the Mielke checkerboard lattice, emphasizing the role of the quantum metric tensor in the effective mass of Cooper pairs.

## Contribution

It demonstrates how quantum geometry, specifically the quantum metric tensor, underpins superfluidity in a flat-band lattice model, providing new insights into flat-band superfluidity mechanisms.

## Key findings

- Quantum metric tensor influences Cooper pair effective mass.
- Flat-band superfluidity arises from quantum-geometric effects.
- Mean-field BCS correlations are dominant in the model.

## Abstract

The Mielke checkerboard is known to be one of the simplest two-band lattice models exhibiting an energetically flat band that is in touch with a quadratically dispersive band in the reciprocal space, i.e., its flat band is not isolated. Motivated by the growing interest in understanding the origins of flat-band superfluidity in various contexts, here we provide an in-depth analysis showing how the mean-field BCS correlations prevail in this particular model. Our work reveals the quantum-geometric origin of flat-band superfluidity through uncovering the leading role by a band-structure invariant, i.e., the so-called quantum metric tensor of the single-particle bands, in the inverse effective mass tensor of the Cooper pairs.