The Casimir Effect in Topological Matter

Abstract

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.

Dispersive interactions between standard and Dirac materials and the role of dimensionality

“…Dirac layers whose Fermi levels pass through the Dirac points interact with a force F (2)D ∼ d −4 . We note that a similar expression F (2)D = − 3ge 2 128 πd 4 was obtained for two graphene layers in the retarded Casimir regime, where the Lifshitz formalsim with accurate calculations of the optical response were used [27][28][29][30][31]. Such an expression was also found in other 2D Dirac Here T = 300 K, τ = 0.13 ps, εF = 50 meV, g = 4, vF = c/300 for Dirac materials and g = 2, m = me, ∆ = 1 eV for standard materials.…”

Bulk contributions to the Casimir interaction of Dirac materials

“…Over the recent years, the physics of Casimir interaction [3] emerged as an important instrument for the study of properties of new materials [4,5]. By this motivation, in the present work we investigate the Casimir interaction between Dirac materials.…”

“…Thereby we restrict ourselves to the account of the bulk properties of these materials on the Casimir force as a first step and intend to account for the boundary effects later. The publications on Casimir interactions of various Dirac materials have been reviewed in [4,5]. We like to mention a couple of recent papers, [6][7][8].…”

Casimir forces out of thermal equilibrium near a superconducting transition

“…The extension to plates made of arbitrary materials and at a finite temperature was developed by Lifshitz 2 using the fluctuation-dissipation theorem and Rytov’s theory of thermally induced electromagnetic fields 3 , 4 . Lifshitz theory has been well established through extensive theoretical and experimental work 5 between metals 6 , semiconductors 7 , 8 , phase/change materials 9 , 10 , topological insulators 11 , 12 , among others.…”