Theory of electric field effect on the optical properties of elliptical quantum wire.

Abstract

In the approximation of the effective mass, the electric field effect on the optical properties of the elliptical quantum wire (EQW) was investigated. In an elliptic coordinate system, exact solutions of the Schrödinger equation for an electron in an EQW with hard walls are obtained. The energy spectrum of a quasiparticle consists of energies of even and odd states, whose wave functions are expressed through even and odd Mathieu functions of the first kind. Using these solutions, an orthonormal basis was constructed. The influence of the electric field perpendicular to the quantum wire and parallel to the ellipse's major axis on the energies and forces of the oscillators of quantum electron transitions was calculated using the matrix method. It is shown that the ellipticity of the quantum wire leads to the removal of the degeneracy of the energy spectrum of quasiparticles, since the energies of even and odd electronic states depend differently on the ratio of the EQW semi-axes. The electron's ground state is the even state, which is nondegenerate because there is no corresponding odd state. The electric field has a greater effect on energy states with a lower value of the magnetic quantum number. As the electric field strength increases, the energies of even and odd states shift to the region of lower energies. The distribution of the electron density of the ground state shifts the most in the direction opposite to the direction of the electric field. This leads to a decrease in the strength of the oscillators of quantum transitions with an increase in the intensity of the electric field.