  Supersolid is a long-sought exotic phase of matter, which is characterized by
the coexistence of a diagonal long-range order of solid and an off-diagonal
long-range order of superfluid. Possible candidates to realize such a phase
have been previously considered, including hard-core bosons with long-range
interaction and soft-core bosons. Here we demonstrate that an ultracold atomic
condensate of hard-core bosons with contact interaction can establish a
supersolid phase when simultaneously subjected to spin-orbit coupling and a
spin-dependent periodic potential. This supersolid phase is accompanied by
topologically nontrivial spin textures, and is signaled by the separation of
momentum distribution peaks, which can be detected via time-of-flight
measurements. We also discuss possibilities to produce and observe the
supersolid phase for realistic experimental situations.
