Supersolid structure and excitation spectrum of soft-core bosons in three dimensions

By means of a mean-field method, we have studied the zero-temperature structure and excitation spectrum of a three-dimensional soft-core bosonic system for a value of the interaction strength that favors a crystal structure made of atomic nanoclusters arranged with fcc ordering. In addition to the longitudinal and transverse phonon branches expected for a normal crystal, the excitation spectrum shows a soft mode related to the breaking of gauge symmetry, which signals a partial superfluid character of the solid. Additional evidence of supersolidity is provided by the calculation of the superfluid fraction, which shows a first-order drop, from 1 to 0.4, at the liquid-supersolid transition and a monotonic decrease as the interaction strength parameter is increased. The conditions for the coexistence of the supersolid with the homogeneous superfluid are discussed, and the surface tension of a representative solid-liquid interface is calculated.