A Green's function approach to the Casimir effect on topological insulators with planar symmetry

TL;DR

This paper presents a Green's function method to compute the Casimir stress on topological insulators with planar symmetry, considering various configurations and employing a local stress-energy tensor approach.

Contribution

It introduces a Green's function approach combined with stress-energy tensor analysis to evaluate Casimir effects on topological insulators with planar symmetry, including renormalization.

Findings

Numerical results for Casimir stress on topological insulators

Analysis of the limit with one plate at infinity

Methodology applicable to similar quantum field problems

Abstract

We investigate the Casimir stress on a topological insulator (TI) between two metallic plates. The TI is assumed to be joined to one of the plates and its surface in front of the other is covered by a thin magnetic layer, which turns the TI into a full insulator. We also analyze the limit where one of the plates is sent to infinity yielding the Casimir stress between a conducting plate and a TI. To this end we employ a local approach in terms of the stress-energy tensor of the system, its vacuum expectation value being subsequently evaluated in terms of the appropriate Green's function. Finally, the construction of the renormalised vacuum stress-energy tensor in the region between the plates yields the Casimir stress. Numerical results are also presented.