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

¹ National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University Nanjing 210093, China
² Laboratory of Quantum Engineering and Quantum Materials, ICMP and SPTE, South China Normal University Guangzhou 510006, China
³ Jiangsu Key Laboratory for Optoelectronic Detection of Atmosphere and Ocean, Nanjing University of Information Science and Technology - Nanjing 210044, China
⁴ Collaborative Innovation Center of Advanced Microstructures, Nanjing University - Nanjing 210093, China

^(a) shengli@nju.edu.cn (corresponding author)

Received: 12 February 2022
Accepted: 16 March 2022

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.