Thermomagnetic power factor in GaAs/AlxGa1−xAs superlattices

We present a theoretical investigation of the longitudinal and transverse thermomagnetic power factors in non-degenerate GaAs/Al 𝑥 Ga 1 − 𝑥 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 a tight-binding miniband model, closed-form analytical expressions are derived for the electrical conductivity, thermoelectric, and thermomagnetic transport tensors. The theoretical framework incorporates miniband transport, Bloch oscillations, photon-assisted carrier dynamics, and dynamic localization induced by the high-frequency electric field, providing a unified analytical description of nonlinear thermomagnetic transport in semiconductor superlattices. The analytical results reveal pronounced nonlinear dependences of the longitudinal and off-diagonal thermomagnetic power factors on miniband width, carrier concentration, chemical potential, temperature, magnetic field, and ac-field modulation. The magnetic field couples longitudinal and transverse carrier motion through the Lorentz force, while the high-frequency field modifies miniband transport through photon-assisted processes and Bessel-function modulation. The resulting closed-form expressions provide transparent physical insight into the mechanisms controlling thermomagnetic transport in semiconductor superlattices and complement more computationally intensive first-principles and quantum-transport approaches. The results provide a basis for analysing and controlling longitudinal and transverse thermoelectric responses in engineered semiconductor superlattices. These findings establish a comprehensive theoretical framework for optimizing thermomagnetic energy conversion in semiconductor superlattices and provide practical design guidelines for thermoelectric energy harvesters, thermomagnetic sensors, magnetic-field detectors, and solid-state cooling technologies.