Electronic band crossing in sliding bilayer graphene: Tight-binding calculations and symmetry group representation analysis

TL;DR

This paper investigates the emergence of Dirac points in bilayer graphene's electronic structure, showing how band crossings occur due to symmetry and lattice alignment, affecting the material's topological properties.

Contribution

It combines tight-binding calculations with symmetry group analysis to explain the origin and conditions of Dirac points in sliding bilayer graphene.

Findings

Dirac points emerge near Brillouin zone corners due to band crossings.

Symmetry analysis confirms the topological stability of these Dirac points.

Band crossings are dictated by symmetry compatibility relations.

Abstract

Dirac points are found to emerge due to the crossing of bands in the electronic structure of bilayer graphene for configurations in which the alignment between two hexagonal lattices preserves the parallelism of the armchair/zigzag lines between two layers. On the base of electronic calculations using a tight-binding model for the $\pi$ bands it is shown that the crossing of the energy-band dispersion curves occurs in the vicinity of the corner points of the hexagonal Brillouin zone. Group representation theory analysis confirms the emergence of such Dirac points. It is demonstrated that the band crossings at generic $\mathbf{k}$ points are guaranteed by the compatibility relations between the symmetries of eigenstates at the high-symmetry $\mathbf{k}$ points in the Brillouin zone. The presence of Dirac points governs the geometrical properties of the energy surfaces, and thus the topological structure of the Fermi energy surface and the energy spectrum.