(Quasi-)Quantization of the electrical, thermal, and thermoelectrical conductivities in two and three dimensions

Abstract

Abstract The quantum Hall effect in a 2D electron system expresses a topological invariant, leading to a quantized conductivity. The thermal Hall and thermoelectric Nernst conductances in two dimensions are also reported to be quantized in specific systems. However, a comprehensive study of these quantities within one formalism for quantum Hall systems is so far elusive. In this work, we investigate the Hall, thermal Hall, and Nernst effects analytically and numerically in 2D and 3D. In addition to the quantized values for the Hall and thermal Hall conductances in two dimensions, we also find quasi-quantized values in three dimensions, which are the related 2D quanta scaled by a characteristic length. The Nernst conductivity is not generally quantized. Instead, an integration in energy is required to obtain a universally (quasi-)quantized thermoelectric quantity.