Hofstadter spectrum in a semiconductor moir\'e lattice

TL;DR

This paper provides a theoretical analysis of the Hofstadter spectrum in a WSe2/MoSe2 moiré heterobilayer, highlighting the role of valley Zeeman effect and predicting conditions for observing additional Hofstadter states.

Contribution

It offers the first comprehensive theoretical interpretation of experimental Hofstadter states in TMD moiré systems, emphasizing the impact of valley Zeeman effect and predicting new observable Hofstadter spectra at larger twist angles.

Findings

Valley Zeeman effect significantly influences Hofstadter spectrum shape.

The Hofstadter spectrum of the moiré flat band can be observed at larger twist angles.

The theory suggests potential for studying Hofstadter and correlated insulating states interplay.

Abstract

Recently, the Hofstadter spectrum of a twisted $\mathrm{WSe_2/MoSe_2}$ heterobilayer has been observed in experiment [C. R. Kometter, et al. Nat.Phys.19, 1861 (2023)], but the origin of Hofstadter states remains unclear. Here, we present a comprehensive theoretical interpretation of the observed Hofstadter states by calculating its accurate Hofstadter spectrum. We point out that the valley Zeeman effect, a unique feature of the transition metal dichalcogenide (TMD) materials, plays a crucial role in determining the shape of the Hofstadter spectrum, due to the narrow bandwidth of the moir\'e bands. This is distinct from the graphene-based moir\'e systems. We further predict that the Hofstadter spectrum of the moir\'e flat band, which was not observed in experiment, can be observed in the same system with a larger twist angle $2^\circ\lesssim\theta \lesssim 3^\circ$. Our theory paves the way for further studies of the interplay between the Hofstadter states and correlated insulting states in such moir\'e lattice systems.