Quantum Hall effect and magnetothermoelectric properties in a periodically modulated three-dimensional electron gas

Abstract In a periodically modulated three-dimensional (3D) electron gas subject to a magnetic field, the Hall conductivity exhibits quantized plateaus, which well correspond to the zero values of the transverse conductivity, a clear signature of the emergence of 3D quantum Hall effect (QHE). We develop a semiclassical theory for the 3D QHE system, taking into account the effect of the Landau level broadening and finite temperatures, to calculate the conductivities and thermoelectric transport coefficients. Our theory provides a concise unified theoretical description for the complex oscillation behavior of the conductivities and thermoelectric transport coefficients in a 3D QHE system. It may serve as a valuable assistance for understanding the simultaneously measured electrical and thermoelectric data in experiments.