Semi-parabolic plus semi-inverse squared quantum wells: Nernst coefficient under the influence of intense electromagnetic waves

Abstract

This work presents a comprehensive theoretical study of the quantum Nernst effect (QNE) in semi-parabolic plus semi-inverse squared quantum wells (SPSSQWs) under intense electromagnetic wave (EMW) radiation, by considering both electron–optical phonon and electron–acoustic phonon scattering mechanisms. Using quantum kinetic theory, analytic expressions for the Nernst coefficient (NC) are derived through calculations of electric conductivity tensors and thermodynamic tensors. Numerical results for GaAs/AlGaAs SPSSQWs reveal complex nonlinear behaviors and multi-mode resonance effects that are strongly influenced by confinement asymmetry. Specifically, under dominant electron–optical phonon scattering, the NC exhibits pronounced nonlinear dependence on temperature, magnetic field, EMW frequency, and confinement strength. The resonance peaks are determined by the magneto-phonon resonance condition. Their positions systematically shift toward higher frequencies with increasing magnetic field, EMW frequency, or confinement frequency. Meanwhile, the background level of the Nernst coefficient decreases. In contrast, increasing temperature does not change the peak positions but enhances their amplitudes and broadens their widths. In the regime dominated by electron–acoustic phonon scattering, the QNE shows qualitatively distinct behaviors characterized by pronounced Shubnikov–de Haas (SdH) oscillations. The oscillation amplitude varies significantly with temperature, whereas the period remains nearly constant. In addition, changes in magnetic field, EMW frequency, or confinement frequency lead to simultaneous variations in both amplitude and period, with the period increasing systematically. These findings not only establish a quantitative connection between resonance peak positions and the magneto-phonon resonance condition, but also provide a unified theoretical foundation for controlled manipulation of thermomagnetic transport in SPSSQWs, supporting future experimental validation and the design of advanced thermoelectric and thermomagnetic devices.