Extra Dirac points in the energy spectrum for superlattices on single-layer graphene

TL;DR

This paper explores how superlattice structures on single-layer graphene can generate additional Dirac points in the electronic spectrum, affecting its electronic properties and potential applications.

Contribution

It provides analytical expressions for the emergence and location of extra Dirac points in graphene superlattices with square barriers, including their movement and disappearance conditions.

Findings

Extra Dirac points appear in the energy spectrum of graphene superlattices.

The position of these points depends on barrier and well widths and potential height.

Presence of extra Dirac points influences the density of states and conductivity.

Abstract

We investigate the emergence of extra Dirac points in the electronic structure of a periodically spaced barrier system, i.e., a superlattice, on single-layer graphene, using a Dirac-type Hamiltonian. Using square barriers allows us to find analytic expressions for the occurrence and location of these new Dirac points in k-space and for the renormalization of the electron velocity near them in the low-energy range. In the general case of unequal barrier and well widths the new Dirac points move away from the Fermi level and for given heights of the potential barriers there is a minimum and maximum barrier width outside of which the new Dirac points disappear. The effect of these extra Dirac points on the density of states and on the conductivity is investigated.