Electronic properties of twisted bilayer graphene in high-energy k p-Hamiltonian approximation

Abstract

A model of twisted bilayer graphene has been o ered on the base of developed quasi- relativistic approach with high energy k p-Hamiltonian. Monolayer-graphene twist is accounted as a perturbation of monolayer-graphene Hamiltonian in such a way that at a given point of the Brillouin zone there exists an external non-Abelian gauge eld of another monolayer. Majorana-like resonances have been revealed in the band structure of model at a magic rotation angle M = 1:05 . The simulations have also shown that a superlattice energy gap existing at a rotation angle 1:08 vanishes at a rotation angle 1:0 .