On superflow in solid He 4

Kim and Chan have recently observed nonclassical rotational inertia (NCRI) for solid $^{4}\mathrm{He}$ in Vycor glass, porous gold, and bulk. Their low $T$ value of the superfluid fraction, ${\ensuremath{\rho}}_{s}∕{\ensuremath{\rho}}_{0}\ensuremath{\approx}0.015$, is consistent with what is known of atomic delocalization in this quantum solid. Upon including a lattice mass density ${\ensuremath{\rho}}_{L}$ distinct from the normal fluid density ${\ensuremath{\rho}}_{n}$ (which is zero at $T=0$), the superfluid hydrodynamics becomes consistent with Galilean transformations. From its microscopic definition, ${\ensuremath{\rho}}_{L}$ is temperature dependent. As a consequence, determination of ${\ensuremath{\rho}}_{n}∕{\ensuremath{\rho}}_{0}$ from ${\ensuremath{\rho}}_{s}∕{\ensuremath{\rho}}_{0}$ is not trivial, although a characteristic excitation energy of about $0.35\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ can be extracted from the data. The macroscopic phase inferred from the observation of NCRI suggests quantum vortices, whose properties we discuss. Searches for quantum vortex lines and rings are proposed.