Quantum metric and effective mass of a two-body bound state in a flat band

TL;DR

This paper investigates how the quantum metric influences the effective mass of two-body bound states in flat bands, providing insights into flat band superconductivity and proposing experimental tests.

Contribution

It establishes a connection between the effective mass of bound pairs and a band structure invariant, the quantum metric, in flat band systems.

Findings

Finiteness of the effective mass is determined by the quantum metric.

The results provide a foundation for understanding flat band superconductivity.

An experiment is proposed to test interaction-induced pair motion.

Abstract

We consider two-body bound states in a flat band of a multiband system. The existence of pair dispersion predicts the possibility of breaking the degeneracy of the band and creating order, such as superconductivity. Within a separable interaction potential approximation, we find that finiteness of the effective mass of a bound pair is determined by a band structure invariant, which in the uniform case becomes the quantum metric. The results offer a simple foundation to understand and predict flat band superconductivity. We propose an experiment to test the interaction-induced pair motion.