We report on a fully self-consistent Hartree-Fock calculation of interaction effects on the moiré 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 the gaplessness of which is protected by the topology of the moiré 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 semimetallic and insulating behaviors seen at charge neutrality, and the sample variability of their observation. We also compare with the results of scanning tunneling microscopy measurements near charge neutrality.

• Received 29 March 2020
• Revised 23 November 2020
• Accepted 3 November 2020

DOI:https://doi.org/10.1103/PhysRevResearch.3.013033

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Published by the American Physical Society