Mott insulators in moiré transition metal dichalcogenides at fractional fillings: Slave-rotor mean-field theory

Abstract

In this work, we study a slave-rotor mean-field theory of an extended Hubbard model, applicable to transition metal dichalcogenide moiré 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 moiré heterostructures.

17 pages, 12 figures

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• Chiral spin liquid phase in an optical lattice at mean-field level
• Mott transition and correlation effects on strictly localized states in an octagonal quasicrystal
• Topological strongly correlated phases in orthorhombic diamond lattice compounds
• Localization and topological signatures under periodic twisting
• Spontaneous emergence of altermagnetism in the single-orbital extended Hubbard model