Commensuration and Interlayer Coherence in Twisted Bilayer Graphene

TL;DR

This paper investigates how lattice commensuration affects electronic coherence and spectral properties in twisted bilayer graphene, revealing distinct behaviors based on sublattice symmetry and fault angles.

Contribution

It introduces a long wavelength theory for commensurate faults in twisted bilayer graphene, highlighting the role of sublattice symmetry in spectral characteristics.

Findings

Commensuration precludes massless Dirac behavior near neutrality.

Sublattice exchange symmetry leads to two distinct spectral families.

Sublattice-symmetric faults are typically fully gapped due to pseudospin-orbit coupling.

Abstract

The low energy electronic spectra of rotationally faulted graphene bilayers are studied using a long wavelength theory applicable to general commensurate fault angles. Lattice commensuration requires low energy electronic coherence across a fault and preempts massless Dirac behavior near the neutrality point. Sublattice exchange symmetry distinguishes two families of commensurate faults that have distinct low energy spectra which can be interpreted as energy-renormalized forms of the spectra for the limiting Bernal and AA stacked structures. Sublattice-symmetric faults are generically fully gapped systems due to a pseudospin-orbit coupling appearing in their effective low energy Hamiltonians.