Commensuration and interlayer coherence in twisted bilayer graphene

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 pre-empts 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.