Signatures of Complex Optical Response in Casimir Interactions of Type I and II Weyl Semimetals

TL;DR

This paper explores how the unique electronic and optical properties of Weyl semimetals influence the Casimir interaction, revealing that their topological features have a secondary effect compared to their metallic-like electromagnetic response.

Contribution

It provides a comprehensive analysis of the bulk and surface conductivity tensors of Weyl semimetals and calculates the Casimir energy considering anisotropic boundary conditions.

Findings

Casimir interaction is metallic-like in Weyl semimetals.

Tilting of energy cones affects the magnitude and distance dependence of the Casimir force.

Topology has a secondary role compared to electromagnetic properties.

Abstract

The Casimir interaction is induced by electromagnetic fluctuations between objects and it is strongly dependent upon the electronic and optical properties of the materials making up the objects. Here we investigate this ubiquitous interaction between Weyl semimetals, a class of 3D systems with low energy linear dispersion and nontrivial topology due to symmetry conditions and stemming from separated energy cones. A comprehensive examination of all components of the bulk conductivity tensor as well as the surface conductivity due to the Fermi arc states in real and imaginary frequency domains is presented using the Kubo formalism for Weyl semimetals with different degree of tilting of their linear energy cones. The Casimir energy is calculated using a generalized Lifhsitz approach, for which electromagnetic boundary conditions for anisotropic materials were derived and used. We find that the Casimir interaction between Weyl semimetals is metallic-like and its magnitude and characteristic distance dependence can be modified by the degree of tilting and chemical potential. The nontrivial topology plays a secondary role in the Casimir interaction of these 3D materials and thermal fluctuations are expected to have similar effects as in metallic systems.