Hofstadter spectrum in a semiconductor moiré lattice

Abstract

Recently, the Hofstadter spectrum of a twisted $\mathrm{WS}{\mathrm{e}}_2/MoS{\mathrm{e}}_2$ 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 moiré bands. This is distinct from the graphene-based moiré systems. We further predict that the Hofstadter spectrum of the moiré flat band, which was not observed in experiment, can be observed in the same system with a larger twist angle $2^{\circ }\lesssim \hat{I}¸\lesssim 3^{\circ }$. Our theory paves the way for further studies of the interplay between the Hofstadter states and correlated insulting states in such moiré lattice systems.

7 pages, 4 figures