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

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 a(1) and outer a(2) hexagons. It is found that all energy levels are decreased with increasing a(1). 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 a(1). The influence of a(2)/a(1) on THG is not large when a(2)/a(1) > 2. The THG shifts toward lower energies by increasing impurity position.