# On the nature of the correlated insulator states in twisted bilayer graphene

## TL;DR

This study uses self-consistent Hartree-Fock calculations to analyze the correlated insulator states in twisted bilayer graphene, revealing that gaps can open without breaking certain symmetries and that insulating states at specific fillings do not always show a quantized Hall effect.

## Contribution

It provides a detailed theoretical analysis of the symmetry properties and conditions for gap opening in twisted bilayer graphene's correlated insulator states.

## Key findings

- Gaps open at neutrality over a wide twist angle range.
- Insulating states at certain fillings may not exhibit a quantized Hall effect.
- Gapped states can form without breaking the system's  symmetry.

## Abstract

We use self-consistent Hartree-Fock calculations performed in the full $\pi$-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer graphene (TBG). We find that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system's valley projected ${\cal C}_{2}{\cal T}$ symmetry. Broken spin/valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moir\'e band filling $n = \pm p/4$ with integer $p = 1, 2, 3$, when the twist angle is close to the magic value at which the flat bands are most narrow. Because the magic-angle flat band quasiparticles are isolated from remote band quasiparticles only for effective dielectric constants larger than $ \sim 20$, the gapped states do not necessarily break \CT symmetry and as a consequence the insulating states at $n = \pm 1/4$ and $n = \pm 3/4$ need not exhibit a quantized anomalous Hall effect.