Adiabatic continuity between Hofstadter and Chern insulator states

TL;DR

This paper demonstrates that Chern insulator bands are adiabatically connected to Hofstadter Landau bands, unifying their topological phases and explaining the impact of Berry curvature distribution on fractional topological states.

Contribution

It establishes an adiabatic link between Hofstadter and Chern insulator states, revealing they are different manifestations of the same topological phase.

Findings

Chern insulator bands are adiabatically connected to Hofstadter Landau bands.

Fractional quantum Hall states on Hofstadter lattices are connected to fractional Chern insulator states.

Nonuniform Berry curvature distribution weakens or destroys fractional topological states.

Abstract

We show that the topologically nontrivial bands of Chern insulators are adiabatic cousins of the Landau bands of Hofstadter lattices. We demonstrate adiabatic connection also between several familiar fractional quantum Hall states on Hofstadter lattices and the fractional Chern insulator states in partially filled Chern bands, which implies that they are in fact different manifestations of the same phase. This adiabatic path provides a way of generating many more fractional Chern insulator states and helps clarify that nonuniformity in the distribution of the Berry curvature is responsible for weakening or altogether destroying fractional topological states.