Supersolid He-4 likely has nearly isotropic superflow
Additional Document Info
We extend previous calculations of the zero temperature upper bound for the superfluid fraction fs vs localization, from the fcc lattice to the experimentally realized (for solid He4) hcp and bcc lattices. The superfluid velocity is assumed to be a one-body function, and dependent only on the local density, taken to be a sum over sites of Gaussians of width . Localization is defined as d, with d the nearest-neighbor distance. As expected, for fcc and bcc lattices the superfluid density tensor is proportional to the unit tensor. To numerical accuracy of three places (but no more), the hcp superfluid density tensor is proportional to the unit tensor. This implies that a larger spread in data on fs, if measured on pure crystals, is unlikely to be due to crystal orientation. In addition, to three decimal places (but no more) the curves of fs vs d are the same for both the hcp and fcc cases. An expected value for the localization gives an fs in reasonable agreement with experiment. The bcc lattice has a similar curve of fs vs d, but is generally smaller because the lattice is more dilute. 2006 The American Physical Society.