Fractional Chern Insulators and Competing States in a Twisted MoTe$_2$ Lattice Model

TL;DR

This paper models twisted MoTe2 bilayers to identify and analyze various topological and charge-ordered states, revealing how interactions and symmetry breaking influence their stability and phase transitions.

Contribution

It introduces a detailed lattice model for twisted MoTe2 and uses iDMRG to uncover competing topological and charge density wave states, highlighting the role of spin exchange and band mixing.

Findings

Robust integer and fractional Chern insulators identified

Phase transitions driven by sublattice potential and interaction strength

Spin exchange stabilizes valley-polarized Chern ferromagnet band

Abstract

We construct an interacting lattice model for twisted $\mathrm{MoTe}_{2}$ bilayers at a twist angle of approximately 3.7\degree. We use the infinite density matrix renormalization group (iDMRG) in a cylinder geometry to identify a variety of competing integer and fractional Chern insulators and charge density wave (CDW) states that emerge upon the spontaneous breaking of time reversal symmetry by valley polarization. We use finite-size analysis to establish the robustness of Chern insulating states even in geometries that admit competing CDWs, and explore the phase transitions between these states driven by increasing sublattice potential or interaction strength. Our work highlights the crucial role played by direct spin exchange in stabilizing the parent valley-polarized Chern ferromagnet band, and by the mixing with higher bands in destabilizing CIs/FCIs in favor of CDW orders.