Time-reversal versus chiral symmetry breaking in twisted bilayer graphene

Abstract

By applying a self-consistent Hartree-Fock approximation, we show that the mechanism of dynamical symmetry breaking can account for the insulating phase that develops about the charge neutrality point of twisted bilayer graphene around the magic angle. ($i$) If the Coulomb interaction is screened by metallic gates, the opening of a gap between the lowest-energy valence and conduction bands proceeds through the breakdown of chiral symmetry at strong coupling. Increasing the dielectric screening, however, we find a critical coupling at which chiral symmetry breaking is suppressed, triggering a very strong signal for time-reversal symmetry breaking with Haldane mass. ($ii$) If the long-range tail of the Coulomb interaction is not screened, we see the appearance of yet a different dominant pattern at strong coupling, which is characterized by breaking the time-reversal invariance but with opposite flux in the two sublattices of each carbon layer, with the consequent valley symmetry breaking. In this case a gap is also opened in the Dirac cones, but superposed to the splitting of the degeneracy of the low-energy bands at the $K$ points of the moiré Brillouin zone.

6 pages, 3 figures

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• Unconventional Superconductivity in Magic-Angle Twisted Trilayer Graphene
• Interactions in the 8-orbital model for twisted bilayer graphene
• Flat-band ferromagnetism in twisted bilayer graphene
• Importance of long-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene
• 3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect
• Flat bands, electron interactions and magnetic order in magic-angle mono-trilayer graphene
• Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene
• Theory of plasmonic edge states in chiral bilayer systems
• Strain-induced excitonic instability in twisted bilayer graphene
• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
• Short vs. long range exchange interactions in twisted bilayer graphene
• Cascades in transport and optical conductivity of Twisted Bilayer Graphene
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Prediction of the Hubbard U parameter from scanning tunneling microscopy images of moire systems using image recognition