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.
Highlights
There are three gapped solutions corresponding to SP, VP, and C2T breaking (C2T I) insulators
The degree of C3 breaking measured by χC3 [Eq (8)] for the C2T breaking insulator as a function χC3 for the noninteracting system for 0 |β| 5 × 10−4 is shown in panels (b) and (c) for positive and negative values of β, respectively
We have performed a momentum-space selfconsistent Hartree-Fock analysis to uncover the nature of the symmetry-broken phase in twisted bilayer graphene at charge neutrality
Summary
The discovery of interaction-driven insulating and superconducting behavior in twisted bilayer graphene (TBG) [1,2] has inspired intensive efforts to understand this behavior [3,4,5,6,7,8,9,10,11,12,13,14,15,16] and to find related systems which exhibit similar phenomenology [17,18,19,20,21,22]. A C2T symmetry-breaking insulator, with Chern number ±1 for each spin and valley flavor, was proposed in Ref. Instead of merging and opening a gap as one might normally expect, the Dirac points remain gapless since they carry the same chirality [4], a consequence of descending from the Dirac points of graphene from the same valley for the two layers This topological protection prevents them from annihilating, resulting in a gapless semimetallic state. Our results suggest that these two states are candidate ground states in the presence of very small explicit C3 symmetry breaking which is likely to exist in experiments Further competition between these two phases is likely to be settled by small sample-dependent details, potentially explaining the realization of an insulator in some samples and a semimetal in other samples
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