Superfluid properties of a honeycomb dipolar supersolid

Recent breakthrough experiments on dipolar condensates have reported the creation of supersolids, including two-dimensional arrays of quantum droplets. Droplet arrays are, however, not the only possible non-trivial density arrangement resulting from the interplay of mean-field instability and quantum stabilization. Several other possible density patterns may occur in trapped condensates at higher densities, including the so-called honeycomb supersolid, a phase that exists, as it is also the case of a triangular droplet supersolid, in the thermodynamic limit. We show that compared to droplet supersolids, honeycomb supersolids have a much-enhanced superfluid fraction while keeping a large density contrast, and constitute in this sense a much better dipolar supersolid. However, in contrast to droplet supersolids, quantized vortices cannot be created in a honeycomb supersolid without driving a transition into a so-called labyrinthic phase. We show that the reduced moment of inertia, and with it the superfluid fraction, can be however reliably probed by studying the dynamics following a scissors-like perturbation.