Tunable Casimir Repulsion with Three-Dimensional Topological Insulators

In this Letter, we show that switching between repulsive and attractive Casimir forces by means of external tunable parameters could be realized with two topological insulator plates. We find two regimes where a repulsive (attractive) force is found at small (large) distances between the plates, canceling out at a critical distance. For a frequency range where the effective electromagnetic action is valid, this distance appears at length scales corresponding to $1-ϵ(\omega )\sim (2/\pi )\alpha \theta$.

Figure 1

Different configurations of the Casimir effect with identical TI covered with a thin magnetic layer. (a) The magnetization is of the same sign on each surface, resulting in a case where ${\theta }_1={\theta }_2$ giving Casimir attraction. In (b)–(d) the magnetizations have opposite signs on the surface (${\theta }_1=-{\theta }_2$) leading to attraction when $d>d_m$, repulsion when $d<d_m$, and to a quantum levitation configuration at $d_m$ where the net force is zero.

Figure 2

Casimir energy density [in units of $E_0=A\hslash c/(2\pi {)}^2({\omega }_R/c{)}^3$] as a function of the dimensionless distance $\overline{d}$ for ${\omega }_e/{\omega }_R=0.45$. In (a) ${\theta }_2=-\pi$ is fixed. Whenever $\mathrm{sgn}({\theta }_1)=-\mathrm{sgn}({\theta }_2)$ a minimum ${\overline{d}}_m$ appears, leading to a vanishing net force on the plates. Increasing ${\theta }_1$ within positive values suppresses the minimum shifting ${\overline{d}}_m$ towards lower values (if both signs are equal then only attractive behavior occurs). Complete repulsion is achieved when one of the TMEP is much bigger than the other. (b) The optimal situation ${\theta }_1=-{\theta }_2=\theta$. Different values of $\theta$ show that the minimum is enhanced when the difference between the two values is as small as possible ($\theta =\pi$). Inset: Detailed behavior around the minimum for the case $\theta =3\pi$.

Figure 3

Effect of parameter $ϵ(0)$ with fixed ${\theta }_1=-{\theta }_2=\pi$. The effect of increasing $ϵ(0)$ is to develop a minimum, which shifts to smaller ${\overline{d}}_m$ as $ϵ(0)$ is increased.