Optimal twist angle for a graphene-like bilayer

The first optimal-or 'magic'-angle leading to the nullity of the Dirac/Fermi velocity for twisted bilayer graphene is re-evaluated in the Bistritzer-MacDonald set-up (Bistritzer and MacDonald 2011 Proc. Natl Acad. Sci. 108 12233-7). From the details of that calculation we study the resulting alterations when the properties of the two layers are not exactly the same. A moire combination of lattices without relative rotation but with different spacing lengths may also lead to a vanishing Dirac velocity. Hopping amplitudes can vary as well, and curvature is one of the possible causes for their change. In the case of small curvature values and situations dominated by hopping energy scales, the optimal angle becomes wider than in the 'flat' case.

Automated summary

This study re-evaluates the first optimal or 'magic' angle leading to the nullity of the Dirac/Fermi velocity in twisted bilayer graphene and investigates the consequences when the properties of the two layers are not exactly the same. A moire combination of lattices without relative rotation but with different spacing lengths can also result in a vanishing Dirac velocity. Hopping amplitudes can vary, with curvature being one of the possible causes for their change. In cases of small curvature values and dominance of hopping energy scales, the optimal angle becomes wider compared to the 'flat' case.