Casimir interaction between topological insulators with finite surface band gap

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.

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