Theoretical Study of the Hall Effect in Infinite Semi-parabolic Quantum Wells in the Presence of Electromagnetic Waves by Using Quantum Kinetic Equation

Theoretical study of the Hall effect in an infinite semi-parabolic Quantum Well (ISPQW) in the presence of electromagnetic using the quantum kinetic equation in the case of electron-acoustic phonon scattering. With the quantum kinetic equation method, the electron distribution function is constructed, from which analytic expressions for the conductivity tensor and the Hall coefficient are derived. The results reveal that the Hall coefficient exhibits a nonlinear dependence on temperature T, magnetic field B, electromagnetic wave frequency , and confinement frequency . Numerical calculations are carried out for a GaAs/AlGaAs quantum well, analyzing the influence of external fields and confinement parameters. Notably, the presence of the electromagnetic wave induces quantum oscillations of the Shubnikov–de Haas type and reduces the average value of the Hall coefficient at high magnetic fields. The results contribute to a deeper understanding of the quantum nature of the Hall effect in asymmetric quantum systems and expand the potential applications of low-dimensional semiconductor structures in advanced nanoelectronic and quantum technologies.