The Coexistence of van Hove Singularities and Superlattice Dirac Points in a Slightly Twisted Graphene Bilayer

TL;DR

This paper investigates the electronic structure of slightly twisted graphene bilayers, revealing the coexistence of van Hove singularities and superlattice Dirac points, and explores how strain influences these features.

Contribution

It demonstrates the coexistence of VHSs and superlattice Dirac points in twisted graphene bilayers and analyzes the impact of strain on their electronic structure.

Findings

Coexistence of van Hove singularities and superlattice Dirac points identified.

Strain significantly shifts the position of van Hove singularities.

Different commensurate structures lead to distinct superlattice Dirac point configurations.

Abstract

We consider the electronic structure of a slightly twisted graphene bilayer and show the coexistence of van Hove singularities (VHSs) and superlattice Dirac points in a continuum approximation. The graphene-on-graphene moir\'e pattern gives rise to a periodic electronic potential, which leads to the emergence of the superlattice Dirac points due to the chiral nature of the charge carriers. Owning to the distinguishing real and reciprocal structures, the sublattice exchange even and odd structures of the twisted graphene bilayer (the two types of commensurate structures) result in two different structures of the superlattice Dirac points. We further calculate the effect of a strain on the low-energy electronic structure of the twisted graphene bilayer and demonstrate that the strain affects the position of the VHSs dramatically.