Repulsive Casimir effect in Chern insulators

Abstract

Casimir effect originated from quantum fluctuations of the electromagnetic fields and it plays an important role in modern nano-technology. One useful application is that the repulsive Casimir effect can resolve the troublesome stiction issue in material science. In this work, we investigate the possibility of achieving the repulsive Casimir effect between two identical Chern insulators in two directions, i.e. (i) small finite (non- zero) temperature effect on Casimir–Lifshitz interaction between 2D Chern Insulators with Chern number C = 1 and (ii) the zero temperature Casimir interaction between 2D Chern Insulators with higher Chern number C = 3, 4, 8. We argue that we may not obtain repulsive Casimir force in the case of a small finite (nonzero) temperature effect on the Casimir effect with Chern numbers C = 1. The high temperature regime may diminish the hall conductivity and it tends to generate attractive Casimir force. Moreover, for the zero temperature case with higher Chern numbers C = 3, 4, 8, we suggest that it is possible to get repulsive Casimir force as the hall conductivity of two Chern Insulators has opposing signs.