# Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality

## TL;DR

This paper uses self-consistent Hartree-Fock calculations to explore interaction-driven phases in twisted bilayer graphene at charge neutrality, revealing nematic semimetals and insulators with topological properties influenced by strain.

## Contribution

It identifies and characterizes multiple competing interaction-driven phases in twisted bilayer graphene, including topologically nontrivial semimetals and insulators, under realistic conditions.

## Key findings

- Nematic topological semimetals are stabilized by weak strain.
- Valley Chern insulators and symmetry-breaking insulators are identified.
- Sample variability may explain different experimental observations.

## Abstract

We report on a fully self-consistent Hartree-Fock calculation of interaction effects on the Moir\'e flat bands of twisted bilayer graphene, assuming that valley U(1) symmetry is respected. We use realistic band structures and interactions and focus on the charge neutrality point, where experiments have variously reported either insulating or semimetallic behavior. Restricting the search to orders for which the valley U(1) symmetry remains unbroken, we find three types of self-consistent solutions with competitive ground state energy (i) insulators that break $C_2 {\mathcal T}$ symmetry, including valley Chern insulators (ii) spin or valley polarized insulators and (iii) rotation $C_3$ symmetry breaking semimetals whose gaplessness is protected by the topology of the Moir\'e flat bands. We find that the relative stability of these states can be tuned by weak strains that break $C_3$ rotation. The nematic semimetal and also, somewhat unexpectedly, the $C_2 {\mathcal T}$ breaking insulators, are stabilized by weak strain. These ground states may be related to the semi-metallic and insulating behaviors seen at charge neutrality, and the sample variability of their observation. We also compare with the results of STM measurements near charge neutrality.