van der Waals torque and force between anisotropic topological insulator slabs

Abstract

We investigate the character of the van der Waals (vdW) torque and force between two coplanar and dielectrically anisotropic topological insulator (TI) slabs separated by a vacuum gap in the non-retardation regime, where the optic axes of the slabs are each perpendicular to the normal direction to the slab-gap interface and also generally differently oriented from each other. We find that in addition to the magnetoelectric coupling strength, the anisotropy can also influence the sign of the vdW force, viz., a repulsive vdW force can become attractive if the anistropy is increased sufficiently. In addition, the vdW force oscillates as a function of the angular difference between the optic axes of the TI slabs, being most repulsive/least attractive (least repulsive/most attractive) for angular differences that are integer (half-integer) multiples of π. Our third finding is that the vdW torque for TI slabs is generally weaker than that for ordinary dielectric slabs. Our work provides the first instance in which the vector potential appears in a calculation of the vdW interaction for which the limit is non-retarded or static.

Perspective on Some Recent and Future Developments in Casimir Interactions

“…The strength and sign of the interaction can be modified using the anisotropy through the off-diagonal elements being suppressed or enhanced with respect to the diagonal terms in the Fresnel reflection matrix. Reference [21] has also found that the van der Waals force oscillates with respect to the angle between the optical axes of two anisotropic TIs, which can lead to van der Waals torque. Interestingly, the torque is weakened when θ 1 and θ 2 have opposite signs.…”

The Casimir Effect in Topological Matter

“…In what follows, we summarize the main results of Ref. [56]. In the non-retardation regime, the Casimir-Lifshitz energy per unit area (effectively the van der Waals energy per unit area) is given by the following:…”

“…Crystalline materials are not dielectrically isotropic in general, i.e., the dielectric permittivity of a crystal tends to have different values along different symmetry (or principal) axes of the medium. The effects of uniaxial dielectric anisotropy (i.e., where the dielectric permittivity of the bulk medium is the same along two principal axes but different along the third, the third axis being called the "optic axis") have been studied in the retardation case for a configuration where the optic axes of the two slabs are both aligned with the normal to the topological insulator surface [51], and also in the non-retardation/van der Waals limit (c → ∞) for a configuration where the optic axes are each perpendicular to the surface normal and also mutually misaligned (see Figure 1) [56]. For the first configuration, where the optic axes are aligned with the surface normals, it is found in Ref.…”

“…Such a torque arises, owing to a dielectric mismatch in the azimuthal direction, in the same way that a force arises due to a dielectric mismatch in the surface normal direction. The behavior of the torque has been studied in the non-retardation regime [56], though not in the retardation regime. For the case of retardation, an extra complication arises due to the presence of an extraordinary wave contribution (in addition to the ordinary one) to the Casimir-Lifshitz energy [58].…”

“…In the figure, we only show a finite slice of the slabs, which are assumed to have infinitely large thicknesses and cross-sectional areas. Figure adapted from Ref [56]…”