Superfluidity of Periodic Solids

Leggett's investigation of the superfluid density of solids has been extended. By employing plane waves as a basis set, one can obtain the superfluid fraction $\frac{{\rho }_s}{{\rho }_0}$ as a function of the localization parameter. Solid ${\mathrm{He}}^4$ is estimated to have a $\frac{{\rho }_s}{{\rho }_0}$ between 0.05 and 0.2 at zero temperature. This approach also sheds light on the superfluidity of thin films and the "index of refraction" of fourth-sound chambers.