Theoretical study of Magnetoresistance Oscillations in Semi-parabolic Plus Semi-inverse Squared Quantum Wells in the Presence of Intense Electromagnetic Waves

Magnetoresistance oscillations in semiconductor quantum wells, with the semi-parabolic plus semi-inverse squared potential, under the influence of intense electromagnetic waves (IEMW), is studied theoretically. Analytical expression for the longitudinal magnetoresistance (LMR) is derived from the quantum kinetic equation for electrons, using the Fr\"ohlich Hamiltonian of the electron-acoustic phonon system. Numerical calculation results show the complex dependence of LMR on the parameters of the external field (electric, magnetic field and temperature) as well as the structure parameters of the confinement potential. In the absence of IMEW, Shubnikov-de Haas (SdH) oscillations appear with amplitudes that decrease with temperature in agreement with previous theoretical and experimental results. In the presence of IEMW, the SdH oscillations appear in beats with amplitudes that increase with the intensity of the IEMW. SdH oscillations under the influence of electromagnetic waves are called microwave-induced magnetoresistance oscillations. The maximum and minimum peaks appear at the positions where the IEMW frequencies are integer and half-integer values of the cyclotron frequency, respectively. In addition, the structural parameters of the quantum well such as the confinement frequency and the geometrical parameters have a significant influence on the LMR as well as the SdH oscillations. When the confinement frequency is small, the two-dimensional electronic system in the quantum well behaves as a bulk semiconductor, resulting in the absence of SdH oscillations. In addition, the LMR increases with the geometrical parameter $\beta_z$ of the quantum well. The obtained results provide a solid theoretical foundation for the possibility of controlling SdH oscillations by IEMW as well as the structural properties of materials in future experimental observations.