Distance-dependent sign-reversal in the Casimir-Lifshitz torque

TL;DR

This paper reveals a distance-dependent sign-reversal in the Casimir-Lifshitz torque between anisotropic slabs, showing how the preferred alignment of their principal axes changes with separation distance.

Contribution

It introduces the concept of a critical distance where the Casimir-Lifshitz torque's direction reverses, and provides a perturbative and exact analysis for biaxial and uniaxial materials.

Findings

Sign-reversal occurs at a specific critical distance $a_c$.

The sign-reversal depends on the frequency where in-plane polarizabilities are equal.

The effect disappears in the nonretarded limit.

Abstract

The Casimir-Lifshitz torque between two biaxially polarizable anisotropic planar slabs is shown to exhibit a non-trivial sign-reversal in its rotational sense. The critical distance $a_c$ between the slabs that marks this reversal is characterized by the frequency $\omega_c\!\sim \!c/2a_c$ at which the in-planar polarizabilities along the two principal axes are equal. The two materials seek to align their principal axes of polarizabilities in one direction below $a_c$, while above $a_c$ their axes try to align rotated perpendicular relative to their previous minimum energy orientation. The sign-reversal disappears in the nonretarded limit. Our perturbative result, derived for the case when the differences in the relative polarizabilities are small, matches excellently with the exact theory for uniaxial materials. We illustrate our results for black phosphorus and phosphorene.