Hartree-Fock study of the moir\'e Hubbard model for twisted bilayer transition metal dichalcogenides

TL;DR

This paper uses Hartree-Fock approximation to analyze the moiré Hubbard model in twisted bilayer transition metal dichalcogenides, revealing phase diagrams and effects of spin-orbit coupling, inversion symmetry breaking, and magnetic fields.

Contribution

It provides a comprehensive mean-field analysis of the moiré Hubbard model, including magnetic phases, metal-insulator transitions, and the influence of various tunable parameters.

Findings

Mapped magnetic and metal-insulator phase diagrams

Identified effects of spin-orbit coupling and inversion symmetry breaking

Assessed impact of magnetic fields on spin and orbital properties

Abstract

Twisted bilayer transition metal dichalcogenides have emerged as important model systems for the investigation of correlated electron physics because their interaction strength, carrier concentration, band structure, and inversion symmetry breaking are controllable by device fabrication, twist angle, and most importantly, gate voltage, which can be varied in situ. The low energy physics of some of these materials has been shown to be described by a "moir\'e Hubbard model" generalized from the usual Hubbard model by the addition of strong, tunable spin orbit coupling and inversion symmetry breaking. In this work, we use a Hartree-Fock approximation to reach a comprehensive understanding of the moir\'e Hubbard model on the mean field level. We determine the magnetic and metal-insulator phase diagrams, and assess the effects of spin orbit coupling, inversion symmetry breaking, and the tunable van Hove singularity. We also consider the spin and orbital effects of applied magnetic fields. This work provides guidance for experiments and sets the stage for beyond mean-field calculations.