Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer ${\mathrm{WSe}}_{2}$

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Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer ${WSe}_{2}$

Haining Pan, Fengcheng Wu, and Sankar Das Sarma

Phys. Rev. Research 2, 033087 – Published 16 July 2020

Abstract

We present a theoretical study of single-particle and many-body properties of twisted bilayer ${WSe}_{2}$ . For single-particle physics, we calculate the band topological phase diagram and electron local density of states (LDOS), which are found to be correlated. By comparing our theoretical LDOS with those measured by scanning tunneling microscopy, we comment on the possible topological nature of the first moiré valence band. For many-body physics, we construct a generalized Hubbard model on a triangular lattice based on the calculated single-particle moiré bands. We show that a layer potential difference, arising, for example, from an applied electric field, can drastically change the noninteracting moiré bands, tune the spin-orbit coupling in the Hubbard model, control the charge excitation gap of the Mott insulator at half-filling, and generate an effective Dzyaloshinskii-Moriya interaction in the effective Heisenberg model for the Mott insulator. Our theoretical results agree with transport experiments on the same system in several key aspects, and establish twisted bilayer ${WSe}_{2}$ as a highly tunable system for studying and simulating strongly correlated phenomena in the Hubbard model.

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Received 26 April 2020
Revised 28 June 2020
Accepted 30 June 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033087

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society