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.

23 pages, 10 figures

References in corpus (3)

• The electronic properties of graphene
• Quantum Unfolding: A program for unfolding electronic energy bands of materials
• Projection operator approach to unfolding supercell band structures

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• Emergent phenomena in Nature: a paradox with Theory?