Quantum mechanics

Ground state

Graphene

Mirror symmetry

Band gap

Physics

Bilayer graphene

Topological insulator

Semimetal

Condensed matter physics

Charge (physics)

Optoelectronics

Insulator (electricity)

Physical Review Research

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 C2T symmetry, including valley Chern insulators; (ii) spin- or valley-polarized insulators; and (iii) rotation C3 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 C3 rotation. The nematic semimetal and also, somewhat unexpectedly, the C2T 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 2020Revised 23 November 2020Accepted 3 November 2020DOI:https://doi.org/10.1103/PhysRevResearch.3.013033Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasSymmetry protected topological statesTopological materialsPhysical Systems2-dimensional systemsDirac semimetalGrapheneMott insulatorsStrongly correlated systemsTechniquesHartree-Fock methodsCondensed Matter, Materials & Applied Physics

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