# Disorder-induced Chern insulator in Harper--Hofstadter--Hatsugai model

## TL;DR

This paper investigates how disorder can induce a topological Chern insulator phase in the Harper--Hofstadter--Hatsugai model, revealing disorder's role in creating topological states even when absent in the clean system.

## Contribution

It demonstrates that disorder can induce a Chern insulating phase in the HHH model and explores the effects of different disorder types on topological properties.

## Key findings

- Disorder modifies the gap closing behavior of the system.
- Disorder induces a Chern insulator phase in the trivial regime.
- Moderately strong disorder increases revival events of the Chern insulator.

## Abstract

We study the effects of disorder on the topological Chern insulating phase in the Harper--Hofstadter--Hatsugai (HHH) model. The model with half flux has a bulk band gap and thus exhibits a nontrivial topological phase. We consider two typical types of disorder: on-site random disorder and the Aubry--Andre type quasi-periodic potential. Using the coupling matrix method, we clarify the global topological phase diagram in terms of the Chern number. The disorder modifies the gap closing behavior of the system. This modification induces the Chern insulating phase even in the trivial phase parameter regime of the system in the clean limit. Moreover, we consider an interacting Rice--Mele model with disorder, which can be obtained by dimensional reduction of the HHH model. Moderately strong disorder leads to an increase in revival events of the Chern insulator at a specific parameter point.