We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids, which possess surface or bulk electronic band structures with nontrivial topologies, which can be evinced through optical properties that are characterizable in terms of nonzero topological invariants. The examples we review are three-dimensional magnetic topological insulators, two-dimensional Chern insulators, graphene monolayers exhibiting the relativistic quantum Hall effect, and time reversal symmetry-broken Weyl semimetals, which are fascinating systems in the context of Casimir physics. Firstly, this is for the reason that they possess electromagnetic properties characterizable by axial vectors (because of time reversal symmetry breaking), and, depending on the mutual orientation of a pair of such axial vectors, two systems can experience a repulsive Casimir–Lifshitz force, even though they may be dielectrically identical. Secondly, the repulsion thus generated is potentially robust against weak disorder, as such repulsion is associated with the Hall conductivity that is topologically protected in the zero-frequency limit. Finally, the far-field low-temperature behavior of the Casimir force of such systems can provide signatures of topological quantization.

中文翻译：

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拓扑物质中的卡西米尔效应

我们概述了过去十年中在电子拓扑材料中的 Casimir 相互作用方面所做的工作，我们的重点是固体，它具有具有非平凡拓扑的表面或体电子能带结构，可以通过可表征的光学特性来证明非零拓扑不变量项。我们回顾的例子是三维磁性拓扑绝缘体、二维陈绝缘体、表现出相对论量子霍尔效应的石墨烯单层和时间反转对称性破缺的外尔半金属，它们是卡西米尔物理学背景下的迷人系统。首先，这是因为它们具有由轴向量表征的电磁特性（因为时间反转对称性破坏），并且，根据一对这样的轴向矢量的相互方向，两个系统可能会受到排斥的 Casimir-Lifshitz 力，即使它们的介电性可能相同。其次，由此产生的排斥力对于弱无序具有潜在的鲁棒性，因为这种排斥力与霍尔电导率相关，霍尔电导率在零频率限制中受到拓扑保护。最后，这种系统的卡西米尔力的远场低温行为可以提供拓扑量化的特征。