The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivity σxy of a two-dimensional electron system is exactly quantized. But what happens to the QHE in three dimensions (3D)? Experiments over the past 40 years showed that some of the remarkable physics of the QHE, in particular plateau-like Hall conductivities σxy accompanied by minima in the longitudinal resistivity ρxx , can also be found in 3D materials. However, since typically ρxx remains finite and a quantitative relation between σxy and the conductance quantum e2/h could not be established, the role of quantum Hall physics in 3D remains unsettled. Following a recent series of exciting experiments, the QHE in 3D has now returned to the center stage. Here, we summarize the leap in understanding of 3D matter in magnetic fields emerging from these experiments.

中文翻译：

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量子霍尔物理学和三个维度

1980 年量子霍尔效应 (QHE) 的发现标志着凝聚态物理学的一个转折点：在适当的实验条件下，霍尔电导率 σX是 二维电子系统的量子化。但是 QHE 在三维 (3D) 中会发生什么变化？过去 40 年的实验表明，QHE 的一些非凡物理特性，特别是类平台霍尔电导率 σX是 伴有纵向电阻率的最小值 ρXX , 也可以在 3D 材料中找到。然而，由于通常 ρXX 仍然是有限的，并且之间存在定量关系 σX是 和电导量子 电子2个/H 无法确定，量子霍尔物理学在 3D 中的作用仍未确定。在最近一系列激动人心的实验之后，3D 中的 QHE 现在又回到了中心舞台。在这里，我们总结了从这些实验中出现的对磁场中 3D 物质理解的飞跃。