Finite-difference calculation of the electronic structure of artificial graphene, the 2D hexagonal AlwGa1-wAs/GaAs structure with tunable interactions

The energy dispersion relation of two dimensional hexagonal lattice of GaAs quantum wires embedded in AlwGa1-wAs matrix, called artificial graphene, was calculated by the finite difference method with periodic boundary conditions. The validity of the finite difference based code was checked by comparing the bound state energies of various two dimensional systems with appropriate boundary conditions with analytic solutions or the results obtained by COMSOL software, which uses the finite element method, and a very good agreement was found. The energy dispersion relation calculated for artificial graphene structure shows massless Dirac particles, characteristic for real graphene. Therefore, artificial graphene-like structures have properties similar to those of real graphene, and are tailorable by appropriate structure engineering.