Origin of the Repulsive Casimir Force in Giant Polarization-Interconversion Materials

Achieving strong repulsive Casimir forces through engineered coatings can pave the way for micro- and nanoelectromechanical applications where adhesive forces currently cause reliability issues. Here, we exploit Lifshitz theory to identify the requirements for repulsive Casimir forces in gyrotropic media for two limiting cases (ultrastrong gyroelectric and nongyroelectric). We show that the origin of repulsive force in media with strong gyrotropy such as Weyl semimetals arises from the giant interconversion of polarization of vacuum fluctuations.

Figure 1

Weyl semimetals are strong gyrotropic media whose gyrotropy axis is along the direction of the associated momentum-separation vector $b$ of two Weyl nodes. (a) We show that for two plates with parallel gyrotropy axes, the Casimir force between the plates can become repulsive. (b) For plates with antiparallel gyrotropy axes, the Casimir force is always attractive.

Figure 2

Casimir pressure as a function of the distance, $d$, between a gyrotropic plate and a silicon plate. The dielectric constant of the gyrotropic plate is determined from the magnetoplasma model. Note that the Casimir force is always negative (attractive). When ${ϵ}_b$ decreases from 1.1 to 1, the Casimir force is greatly suppressed.

Figure 3

Casimir pressure as a function of the distance, $d$, between two Weyl-semimetal plates. Note that for the blue dash-dotted curve, the two gyroaxis are antiparallel, we have $r_{sp1}=r_{ps2}$, and the Casimir force is always attractive. For the other three curves, the two gyroaxes are parallel, we have $r_{sp1}=-r_{ps2}$, the Casimir force is tuned from attractive to repulsive. The gray dotted curve crosses zero at around $d=0.052\mu \mathrm{m}$ (unstable equilibrium) and the black solid curve crosses zero at around $d=0.41\mu \mathrm{m}$ (stable equilibrium). For the red dashed curve, the Casimir force is always repulsive.

Figure 4

The integrand ($k_x\times \{-[\mathrm{\partial }\mathrm{Ln}(L)/\mathrm{\partial }d]\}$) in Eq. (2) [shown in (a),(b)] and the associated reflection coefficients [shown in (c),(d)] as a function of $k_x$. We set the Matsubara frequency at $n=1$ and choose parameters the same as those of the black and gray curves in Fig. 3. We use the red (blue) color to denote the repulsive (attractive) contribution to the Casimir force, respectively, in (a),(b).