Calculation of 2D electronic band structure using matrix mechanics

Abstract

We extend previous work applying elementary matrix mechanics to one-dimensional periodic arrays (to generate energy bands) to two-dimensional arrays. We generate band structures for the square lattice "2D Kronig-Penney model" (square wells), muffin-tin potential (cylindrical wells), and Gaussian wells. We then apply the method to periodic arrays of more than one atomic site in a unit cell, in particular, the case of materials with hexagonal lattices like graphene. These straightforward extensions of undergraduate-level calculations allow students to readily determine band structures of current research interest.