Anti-topological crystal and non-Abelian liquid in twisted semiconductor bilayers

TL;DR

This paper explores a novel anti-topological electron crystal in twisted bilayer MoTe2, which competes with non-Abelian fractional Chern insulators and features unique Chern number properties.

Contribution

It introduces the concept of anti-topological crystals with zero net Chern number, contrasting with conventional topological crystals, in twisted bilayer systems.

Findings

Anti-topological crystals can have zero Chern number due to band contributions.

These crystals compete with non-Abelian fractional Chern insulators.

The phenomenon depends on twist angle and microscopic details.

Abstract

We show that electron crystals compete closely with non-Abelian fractional Chern insulators in the half-filled second moir\'e band of twisted bilayer MoTe$_2$. Depending on the twist angle and microscopic model, these crystals can have non-zero or zero Chern numbers $C$. The $C=0$ crystal occurs because contributions to the total Chern number from the full first band (+1) and half-full second band (-1) cancel. This is counterintuitive because the first two non-interacting bands in a given valley have the same Chern number $+1$. For these two reasons, we call this crystal an anti-topological crystal. The anti-topological crystal is a novel type of electron crystal that may occur in systems with multiple Chern bands at filling factors $n>1$.