Hall effect in an infinite semi-parabolic plus semi-inverse squared quantum wells in the presence of a strong electromagnetic wave

Abstract

The Hall effect in infinite Semi-parabolic Plus Semi-inverse Squared Quantum wells (ISPPSISQW) in the presence of a strong Electromagnetic Wave(EMW) is theoretically investigated by using the Quantum Kinetic Equation. The system is subjected to a strong EMW \(\vec{E}(t)=\left(E_0 \sin \Omega t\right) \vec{e}_y\), a magnetic field \(\vec{B}=B \vec{e}_z\), and a cross DC electric field \(\vec{E}=E \vec{e}_x\). The electron-optical phonon scattering is considered. The general expression of the Hall coefficient is presented as a function of the temperature, the external magnetic field, the photon energy, and the intensity of the strong EMW as well as characteristic parameters of ISPPSISQW. The theoretical result for a specific GaAs/GaAsAl ISPPSISQW is obtained by using a numerical method. The computational result demonstrates that the maximum peaks appear satisfying the magneto-phonon-photon resonance condition. For the dependence of Hall coefficient on the magnetic field B : when temperature changes, the resonance peak's position is unaffected by temperature variations; and when confinement frequency increases, the Hall coefficient peak increases in magnitude and the position of the peak shifts towards the smaller magnetic field B. For dependence of Hall Coefficient on the electromagnetic wave frequency: when temperature changes, the peak decreases but the position of the peak does not change; and when increasing confinement frequency, the magnitude of the peak increases and the peak is blue-shifted; and when the external magnetic field \(B\) is increased, the magnitude of the Hall coefficient increases, and the peak position is blue-shifted (i.e. shifted towards higher frequencies).