The Casimir Effect in Topological Matter

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