Chern Bands' Optimally Localized Wannier Functions and Fractional Chern Insulators

TL;DR

This paper introduces a new method for constructing optimally localized Wannier functions in Chern bands, facilitating the study of fractional Chern insulators and their interaction channels.

Contribution

It presents a general approach to generate localized Wannier functions with an optimal gauge choice, applicable to various lattice models like kagome.

Findings

Successfully constructed Wannier functions for kagome lattice.

Identified interaction channels favorable for fractional Chern insulators.

Discussed broader implications for correlations and topology.

Abstract

Recent development on fractional Chern insulators and proximate phases call for a real space representation of isolated Chern bands. Here we propose a new method for a general construction of optimally localized Wannier functions from such Chern bands. We do so through an optimal gauge choice of the Bloch states of a Chern band with the singularity placed at any desired position in momentum space. We apply this method to construct the optimally localized Wannier functions for kagome lattice, and use it to identify channels of interactions that are favorable to the development of fractional Chern insulators. Implications of the approach for the interplay between correlations and topology in broader contexts are discussed.