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.

二维电子系统中的量子霍尔效应表达了拓扑不变量，导致了量化的电导率。据报道，二维的热霍尔和热电能斯特电导也在特定系统中被量化。然而，迄今为止，在量子霍尔系统的一种形式中对这些量的全面研究是难以捉摸的。在这项工作中，我们在 2D 和 3D 中分析和数值研究了霍尔效应、热霍尔效应和能斯特效应。除了二维霍尔电导和热霍尔电导的量化值外，我们还发现了三个维度的准量化值，它们是按特征长度缩放的相关二维量子。能斯特电导率通常不量化。反而，