Casimir interaction between topological insulators with finite surface band gap

TL;DR

This paper investigates how the Casimir force between topological insulators varies with surface band gap and separation, revealing conditions for attractive and repulsive interactions based on the band gap magnitude.

Contribution

It provides a detailed analysis of the Casimir interaction considering finite surface band gaps, identifying a critical gap value that determines force sign changes.

Findings

Casimir force is attractive at small gaps for small band gaps.

A critical band gap value $m_c$ exists, beyond which the force becomes repulsive.

Force behavior transitions from attractive to repulsive depending on surface band gap and separation.

Abstract

Casimir interaction between topological insulators with opposite topological magnetoelectric polarizabilities and finite surface band gaps has been investigated. For large surface band gap limit$(m\rightarrow\infty)$, we can obtain results given in [Phys. Rev. Lett. \textbf{106}, 020403 (2011)]. For small surface band gap limit$(m\rightarrow0)$, Casimir interaction between topological insulators is attractive and analogy to ideal mental in short separation limit. Generally, there is a critical value $m_c$ and when the surface band gap is greater than the critical value, the Casimir force is repulsive in an intermediate separation region. We estimate the critical surface band gap $m_c \sim 1/(2a)$, where $a$ is a critical separation where Casimir force vanishes.