Selective Rotation and Attractive Persistent Currents in Anti-Dipolar Ring Supersolids

A repulsively interacting Bose-Einstein condensate on a ring is well known to show persistent currents. For attractive interactions, however, a bound state may form that renders the rotation classical. Here we show that in a multiply-connected confinement, the strong in-plane attraction of an {\it anti-dipolar }condensate can form stacks of ring-shaped droplets which may coherently overlap to form a supersolid along the azimuthal symmetry axis of the system. Intriguingly, the functional behavior of the energy-angular momentum dispersion of the anti-dipolar ring condensate differs from that of a usual repulsive superfluid. The periodic maxima between persistent flow and the non-rotating ground state flatten significantly and the typical pronounced cusps in the energy dispersion also occur in the rotationally symmetric supersolid state. A weak link results in the reduction of this minimum, shifting it to smaller angular momenta. With an asymmetric link potential one can selectively induce superfluid and rigid-body rotation in different layers within the same system. This intriguing setup offers new perspectives for atomtronics applications.