On electron propagation in triangular graphene quantum dots

Abstract

Tight-binding models of electron propagation in single-layer triangular graphene quantum dots with armchair and zigzag edges are developed. The electron hoppings to the nearest and next-to-nearest neighbours on the honeycomb lattice as well as interactions with the confining Dirichlet and Neumann walls are incorporated into the resulting tight-binding Hamiltonians. Associated to the irreducible crystallographic root system A 2, the armchair and zigzag honeycomb Weyl orbit functions together with the related discrete Fourier–Weyl transforms provide explicit exact forms of the electron wave functions and energy spectra. The electronic probability densities corresponding to the armchair and zigzag dots are evaluated and their contrasting behaviour exemplified.