Designing (higher) Hall crystals

TL;DR

This paper proposes a new platform using 2D semiconductors or graphene with magnetic fields and modulations to realize interaction-driven Hall crystals with various Chern numbers, including higher values.

Contribution

It introduces a novel method to create interaction-induced Hall crystals with diverse topological properties using moiré or dielectric engineering.

Findings

Hall crystals with various Chern numbers are realized.

The phases are stable across continuous ranges of filling and magnetic field.

A unified phase diagram explains the phenomena.

Abstract

We introduce a novel platform for realizing interaction-induced Hall crystals with diverse Chern numbers $C$. This platform consists of a two-dimensional semiconductor or graphene subjected to an out-of-plane magnetic field and a one-dimensional modulation, which can be realized by moir\'e or dielectric engineering. We show that interactions drive the system to spontaneously break the residual translational symmetry, resulting in Hall crystals with various $C$ (including $|C|>1$). Remarkably, these phases persist across continuous ranges of filling and magnetic field, and the global phase diagram can be understood in a unified manner.