Fractional Chern Insulators in Twisted Bilayer MoTe$_2$: A Composite Fermion Perspective

TL;DR

This paper uses a composite fermion approach to analyze fractional Chern insulators in twisted bilayer MoTe$_2$, revealing a sequence of topological states, explaining experimental observations, and uncovering new fractal and quantum phenomena.

Contribution

It introduces a composite fermion framework to understand FCIs in twisted bilayer MoTe$_2$, linking fractional Hall conductivities to Chern numbers and revealing new fractal states and phase transitions.

Findings

Identified a sequence of FCIs with specific fractional Hall conductivities.

Explained experimental observations of FCIs at certain fractional fillings.

Discovered new fractal FCI states and phenomena in the Hofstadter spectrum.

Abstract

The discovery of Fractional Chern Insulators (FCIs) in twisted bilayer MoTe$_2$ has sparked significant interest in fractional topological matter without external magnetic fields. Unlike the flat dispersion of Landau levels, moir\'e electronic states are influenced by lattice effects within a nanometer-scale superlattice. This study examines the impact of these lattice effects on the topological phases in twisted bilayer MoTe$_2$, uncovering a family of FCIs with Abelian anyonic quasiparticles. Using a composite fermion approach, we identify a sequence of FCIs with fractional Hall conductivities $\sigma_{xy} = \frac{C}{2C + 1} \frac{e^2}{h}$ linked to partial filling $\nu_{\,\text{h}}$ of holes of the topmost moir\'e valence band. These states emerge from incompressible composite fermion bands of Chern number $C$ within a complex Hofstadter spectrum. This approach explains FCIs with Hall conductivities $\sigma_{xy} = (2/3) e^2/h$ and $\sigma_{xy} = (3/5) e^2/h$ at fractional fillings $\nu_{\,\text{h}} = 2/3$ and $\nu_{\,\text{h}} = 3/5$ observed in experiments, and uncovers other fractal FCI states. The Hofstadter spectrum reveals new phenomena, distinct from Landau levels, including a higher-order Van Hove singularity (HOVHS) at half-filling, leading to novel quantum phase transitions. This work offers a comprehensive framework for understanding FCIs in transition metal dichalcogenide moir\'e systems and highlights mechanisms for topological quantum criticality.