Fractional quantum anomalous Hall and anyon density-wave halo in a minimal interacting lattice model of twisted bilayer MoTe$_2$

TL;DR

This paper uses large-scale DMRG simulations to study fractional quantum anomalous Hall states in twisted bilayer MoTe$_2$, revealing robust topological phases, anyon excitations, and charge-ordered states, enriching understanding of correlated topological phenomena in moiré materials.

Contribution

It provides the first comprehensive numerical evidence of FQAH states, anyon density-wave halos, and a phase diagram with charge orderings in a minimal lattice model of twisted bilayer MoTe$_2$.

Findings

Robust FQAH ground states at filling $ u=-2/3$.

Evidence for anyon excitations with fractional charge.

Discovery of charge-ordered states including QAHC.

Abstract

The experimental discovery of fractional quantum anomalous Hall (FQAH) states in tunable moir\'e superlattices has sparked intense interest in exploring the interplay between topological order and symmetry breaking phases. In this paper, we present a comprehensive numerical study of this interplay through large-scale density matrix renormalization group (DMRG) simulations on a minimal two-band lattice model of twisted bilayer MoTe$_2$ at filling $\nu=-2/3$. We find robust FQAH ground states and provide clear numerical evidences for anyon excitations with fractional charge and pronounced real-space density modulations, directly supporting the recently proposed anyon density-wave halo picture. We also map out the displacement field dependent phase diagram, uncovering a rich landscape of charge ordered states emerging from the FQAH, including a quantum anomalous Hall crystal (QAHC) with an integer quantized Hall conductance. We expect our work to inspire further research interest of intertwined correlated topological phases in moir\'e systems.