Phase-induced vortex pinning in rotating supersolid dipolar systems

We analyze the pinning of vortices for a stationary rotating dipolar supersolid along the low-density paths between droplets as a function of the rotation frequency. We restrict ourselves to the stationary configurations of vortices with the same symmetry as that of the array of droplets. In particular, such an analysis clearly reveals that vortices are not only pinned at local density minima, but instead their coordinates are smooth functions of the rotation frequency. Our approach to explaining such a behavior exploits the fact that the wave function of each rotating droplet acquires a linear phase on the coordinates. Hence, the relative phases between the nearest neighboring droplets allow us to predict the position of the vortices in the intermediate low-density region. Here, we show that for a droplet distribution forming a triangular lattice, the phases of three neighboring droplets are needed for the correct description of the vortex location. In particular, for our confined system, we demonstrate that the estimate accurately reproduces the extended Gross-Pitaevskii results in the spatial regions where the neighboring droplets are well-defined.