The Casimir Effect in Topological Matter

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.

Automated summary

The study provides an overview of Casimir interactions in electronic topological materials over the past decade, focusing on solids with nontrivial topological band structures. Examples include magnetic topological insulators, Chern insulators, graphene monolayers, and Weyl semimetals, each exhibiting unique Casimir properties due to their topological features. The Casimir force generated in these systems may exhibit repulsive behavior due to the orientation of axial vectors, which is topologically protected against weak disorder and could provide signatures of topological quantization in far-field low-temperature behavior.