Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers

TL;DR

This paper introduces generalized Hofstadter models with color-entangled flat bands of arbitrary Chern numbers, revealing fractional topological phases with unique degeneracy patterns and potential experimental realizations.

Contribution

It constructs new Hofstadter models with higher Chern numbers and analyzes their fractional topological states, connecting them to topological nematic states and dislocation braiding.

Findings

Existence of gapped fractional states with degeneracy depending on lattice size

Mapping models to multilayer systems explains degeneracy patterns

Provides methods to stabilize fractional states in higher Chern bands

Abstract

We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped states at certain filling factors for which the ground-state degeneracy depends on the number of unit cells along one particular direction. This puzzling observation can be understood intuitively by mapping our model to a single-layer or a multilayer system for a given lattice configuration. We discuss the relation between these results and the previously proposed "topological nematic states," in which lattice dislocations have non-Abelian braiding statistics. Our study also provides a systematic way of stabilizing various fractional topological states in $C>1$ flat bands and provides some hints on how to realize such states in experiments.