Band Structures of Symmetrical Graphene Superlattice with Cells of three Regions

TL;DR

This paper investigates the electronic band structures of symmetrical graphene superlattices with three-region cells, revealing bound, unbound, and forbidden zones, and analyzing Dirac points, gaps, and miniband effects.

Contribution

It provides an explicit dispersion relation for such superlattices using the transfer matrix method, including analysis of Dirac points and energy band features.

Findings

Identification of three zones: bound, unbound, and forbidden states.

Enumeration of vertical Dirac points and energy gaps.

Analysis of miniband effects and group velocity anisotropy.

Abstract

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. Using the transfer matrix method, we explicitly determine the dispersion relation in terms of different physical parameters. We numerically analyze such relation and show that there exist three zones: bound, unbound and forbidden states. In the central zone of the band structures, we determine and enumerate the vertical Dirac points, opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.