Mott insulators in moir\'e transition metal dichalcogenides at fractional fillings: Slave-rotor mean-field theory

TL;DR

This paper develops a slave-rotor mean-field theory for extended Hubbard models in moiré transition metal dichalcogenides, revealing various charge and spin states, including Wigner crystals, spin liquids, and dimers, with implications for experiments.

Contribution

It introduces a theoretical framework capturing charge and spin phenomena in moiré TMDs, predicting multiple competing states at fractional fillings.

Findings

Reproduces experimentally observed Wigner crystal states.

Identifies several spin liquid and dimer states at fractional fillings.

Suggests experimental signatures for different quantum states.

Abstract

In this work, we study a slave-rotor mean-field theory of an extended Hubbard model, applicable to transition metal dichalcogenide moir\'e systems, that captures both the formation of Wigner crystals as well as exotic spin states on top of these charge backgrounds. Phase diagrams are mapped out for different choices of long-range Coulomb repulsion strength, reproducing several experimentally found Wigner crystal states. Assuming unbroken time reversal symmetry, we find several spin liquid states as well as dimer states at fractional fillings. While spin dimer states are always found to have the lowest mean field energy, several spin liquid states are energetically competitive and may be stabilized by including gauge fluctuations or further interaction terms. We further discuss possible experimental signatures of these states pertinent to two-dimensional moir\'e heterostructures.