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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 for sufficiently small anisotropy and/or large magnetoelectric
polarizability, the vdW force can become repulsive, and in addition, the 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 \(\pi\). Furthermore, we have found 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.