The energy levels, binding energy and third harmonic generation of a hexagon-shaped quantum wire

Abstract

In this paper, we have studied the effect of impurity on the energy levels and nonlinear optical properties of a hexagon-shaped quantum wire using finite element method (FEM). We have obtained the energy eigenvalues, their corresponding eigenfunctions and third harmonic generation (THG) with and without impurity for different sizes of inner a1 and outer a2 hexagons. It is found that all energy levels are decreased with increasing a1. There is degeneracy between energy levels without impurity. But, there is no degeneracy between the energy levels in the presence of impurity. The dipole matrix elements are increased with enhancing hexagon sizes without impurity. But, these elements have complex behaviors with impurity. The THG increases and shifts toward lower energies by enhancing a1. The influence of a2/a1 on THG is not large when a2/a1 > 2. The THG shifts toward lower energies by increasing impurity position.