Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene

TL;DR

This study uses exact diagonalization to analyze the electronic states of magic-angle twisted bilayer graphene, revealing ferromagnetic and Chern insulator phases depending on band filling, emphasizing the importance of remote band self-energy.

Contribution

It provides the first finite-size exact-diagonalization analysis of MATBG flat bands, highlighting the role of remote band self-energy in correlation effects.

Findings

Ground state is a spin ferromagnet near filling 3>| u|>2.

Chern insulator states with spin, valley, and sublattice polarization near | u|=3.

Remote band self-energy is crucial for accurate correlation descriptions.

Abstract

We report on finite-size exact-diagonalization calculations in a Hilbert space defined by the continuum-model flat moir\'e bands of magic angle twisted bilayer graphene (MATBG). For moir\'e band filling $3>|\nu|>2$, where superconductivity is strongest, we obtain evidence that the ground state is a spin ferromagnet. Near $|\nu|=3$, we find Chern insulator ground states that have spontaneous spin, valley, and sublattice polarization, and demonstrate that the anisotropy energy in this order-parameter space is strongly band-filling-factor dependent. We emphasize that inclusion of the remote band self-energy is necessary for a reliable description of MATBG flat band correlations.