Casimir interaction between topological insulators with finite surface band gap

The Casimir interaction between topological insulators with opposite topological magnetoelectric polarizabilities and finite surface band gaps has been investigated. For a large surface band-gap limit (m -> infinity), we can obtain results given by Grushin and Cortijo [Phys. Rev. Lett. 106, 020403 (2011)]. For a small surface band-gap limit (m -> 0), the Casimir interaction between topological insulators is attractive and in analogy to the ideal mental model in a 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) similar to 1/(2a), in which a is a critical separation where the Casimir force vanishes.