Abstract
The effect of homogeneous electric field on the energy spectrum, wave functions of electron and oscillator strengths of intra-band quantum transitions in a double cylindrical quantum ring (GaAs/Al$_{x}$Ga$_{1-x}$As) is studied within the approximations of effective mass and rectangular potentials. The calculations are performed using the method of expansion of quasiparticle wave function over a complete set of cylindrical wave functions obtained as exact solutions of Schr\"odinger equation for an electron in a nanostructure without electric field. It is shown that the electric field essentially affects the electron localization in the rings of a nanostructure. Herein, the electron energies and oscillator strengths of intra-band quantum transitions non-monotonously depend on the intensity of electric field.
Highlights
Multilayered semiconductor nanostructures are studied both theoretically and experimentally for quite a long time
The electron energy spectrum and oscillator strengths of intra-band quantum transitions in a double quantum ring GaAs/AlxGa1−xAs nanostructure are studied as functions of the electric field intensity (F) within the approximations of effective mass and rectangular potentials
To calculate the energy spectrum and probability densities of the electron location in nano-rings driven by electric field, the stationary Schrödinger equation is solved using the method of expansion of a quasiparticle wave function over a complete set of wave functions in a nanostructure without the electric field
Summary
Multilayered semiconductor nanostructures are studied both theoretically and experimentally for quite a long time. Semiconductor quantum rings occupy a separate place among various types of nanostructures As a rule, they have cylindrical symmetry as well as quantum wires [4]. In [8, 9], the influence of a magnetic field on the energy spectrum of the electron and on the oscillator strengths of its intra-band quantum transitions in GaAs/AlxGa1−xAs rings was studied. It was shown that the electron energies and the oscillator strength of intra-band quantum transitions non-monotonously depend on the induction of the magnetic field. The oscillator strengths of intra-band quantum transitions as functions of the electric field intensity in a double quantum ring GaAs/AlxGa1−xAs nanostructure are analyzed. 2. Theory of electron energy spectrum and oscillator strengths of intraband quantum transitions in double quantum ring nanostructure driven by electric field. Μ0 , |z| > L/2 or |z| L/2 and 0 ρ ρ0 , ρ1 μ1 , |z| L/2 and ρ0 < ρ < ρ1 , ρ2 < ρ ρ3
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