Quantum metric induced hole dispersion and emergent particle-hole symmetry in topological flat bands

TL;DR

This paper reveals a linear relationship between hole dispersion and quantum geometry in flat bands, enabling the engineering of particle-hole symmetry, which advances understanding of quantum geometry's role in topological flat band systems.

Contribution

It demonstrates a universal linear relationship between hole dispersion and quantum geometry tensor trace, and shows how to engineer particle-hole symmetry in Chern bands using this insight.

Findings

Hole dispersion linearly relates to quantum geometry tensor trace.

Different origins for short-range and long-range interaction effects.

Method to engineer particle-hole symmetry in topological flat bands.

Abstract

The emergent hole dispersion in flat bands is an invaluable platform to study the interplay of quantum geometry and electron-electron interaction with a relatively simple setting. In this work, we find that the hole dispersion in ideal bands has a linear relationship with the trace of the quantum geometry tensor at every $\boldsymbol{k}$-point for a wide range of interactions to a good approximation. Next, we give a microscopic analysis on the hole dispersion and show that the linear relationships for short-range and long-range interactions in $\boldsymbol{k}$-space have different origins. Moreover, we show how to exploit this observation to engineer particle-hole symmetry in a Chern band with fluctuating quantum geometry. Our results will be useful for further studying the physics in particle-hole symmetric flat bands both in theory and in experiment.