Herein, we present a theoretical investigation of thermomagnetic transport and the Nernst effect in nondegenerate GaAs/Al ₓ Ga ₁-ₗ As semiconductor superlattices subjected simultaneously to dc and high-frequency ac electric fields, a transverse magnetic field, and an applied temperature gradient. Using the semiclassical Boltzmann transport equation within the constant relaxation-time approximation and the miniband transport model, analytical expressions are derived for the electrical conductivity tensor (₈₊), thermoelectric tensor (₈₊), thermomagnetic power tensor (₈₊), and the corresponding longitudinal and transverse Nernst coefficients, Nₗ and Nₘ. The theoretical formulation incorporates miniband transport, Bloch oscillations, photon-assisted transport, and dynamic localization induced by the high-frequency electric field, providing a unified analytical framework for nonlinear thermomagnetic transport in semiconductor superlattices. The results reveal pronounced nonlinear dependences of the thermomagnetic response on the carrier concentration, miniband width, chemical potential, relaxation time, magnetic field strength, temperature, and the amplitude and frequency of the applied ac electric field. Dynamic localization renormalizes the effective miniband width, leading to oscillatory variations in the electrical conductivity, thermoelectric coefficients, and Nernst response, while the interplay between magnetic field-induced carrier deflection and thermal diffusion enables continuous tuning of both the magnitude and sign of the longitudinal and transverse Nernst coefficients. Comparison with contemporary first-principles and quantum transport approaches demonstrates that the present analytical model provides complementary physical insight into nonequilibrium miniband transport under coupled electric, magnetic, and thermal driving forces. These findings establish a comprehensive theoretical framework for understanding and optimizing thermomagnetic transport in semiconductor superlattices and provide useful guidelines for the design of thermomagnetic sensors, magnetic field detectors, solid-state cooling technologies, and thermoelectric energy-harvesting devices.
Sekyi-Arthur et al. (Thu,) studied this question.