Supercurrent-carrying supersolid in spin-orbit-coupled Bose-Einstein condensates

One of brilliant achievements in spin-orbit-coupled Bose-Einstein condensates is the discovery and observation of the supersolid stripe states. So far, all studied supersolid stripe states do not carry supercurrent. In this paper, we reveal the existence of supercurrent-carrying supersolids in spin-orbit-coupled Bose-Einstein condensates. The supersolid family has a parabolic-like dispersion and carries supercurrent, which is proportional to the quasimomentum. Energetic and dynamical instabilities can break supercurrent-carrying ability of this supersolid family. An insightful interpretation of the dynamical instability of supercurrent-carrying supersolids from the pure plane-wave phase is provided.