Supersolid $^4$He Likely Has Nearly Isotropic Superflow

TL;DR

This study extends calculations of superfluid fraction in solid helium-4 to hcp and bcc lattices, finding nearly isotropic superflow and agreement with experimental data, suggesting superfluidity is largely orientation-independent.

Contribution

It demonstrates that the superfluid density tensor is nearly isotropic in hcp and bcc lattices, extending previous fcc lattice results, and shows the superfluid fraction aligns with experimental observations.

Findings

Superfluid density tensor is nearly isotropic in hcp and bcc lattices.

Superfluid fraction curves are similar for hcp and fcc lattices.

Predicted superfluid fraction agrees with experimental data.

Abstract

We extend previous calculations of the zero temperature superfluid fraction $f_s$ (SFF) {\it vs} localization, from the fcc lattice to the experimentally realized (for solid $^4$He) 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 $\sigma$. Localization is defined as $\sigma/d$, 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 $f_s$, 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 $f_s$ {\it vs} $\sigma/d$ are the same for both the hcp and fcc cases. An expected value for the localization gives an $f_{s}$ in reasonable agreement with experiment. The bcc lattice has a similar curve of $f_s$ {\it vs} $\sigma/d$, but is generally smaller because the lattice is more dilute.