Magic-angle Twisted Bilayer Systems with Quadratic-Band-Touching: Exactly Flat Bands with High-Chern Number

TL;DR

This paper introduces a new twisted bilayer system with quadratic-band-touching points that exhibits exactly flat bands with high Chern numbers, leading to quantum anomalous Hall effects due to Coulomb interactions.

Contribution

It proposes a novel twisted bilayer system with quadratic-band-touching points, revealing exactly flat bands with high Chern numbers and potential for quantum anomalous Hall states.

Findings

Exactly flat bands emerge at magic angles.

Each flat band has a high Chern number of ±2.

Ground state supports quantum anomalous Hall effect with quantized Hall conductivity.

Abstract

Studies of twisted moir\'e systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a twisted bilayer of 2D systems which feature stable quadratic-band-touching points and find exotic physics different from previously studied twisted moir\'e systems. Specifically, we show that exactly flat bands can emerge at magic angles and, more interestingly, each flat band exhibits a high Chern number ($C=\pm 2$). We further consider the effect of Coulomb interactions in such magic-angle twisted systems and find that the ground state supports the quantum anomalous Hall effect with quantized Hall conductivity $2\frac{e^2}{hc}$ at certain filling. Furthermore, the possible physical realization of such twisted bilayer systems will be briefly discussed.