Layer by layer solidification ofHe4in narrow porous media

Abstract

We give a variational Monte Carlo description of $^{4}\mathrm{He}$ filling under pressure a porous material modeled by a smooth cylindrical nanopore. Our trial wave function is a shadow wave function which allows different degrees of correlation between $^{4}\mathrm{He}$ atoms depending on the distance from the pore wall but still preserving the full Bose symmetry. The radial density profile shows a strong layering of the $^{4}\mathrm{He}$ atoms which are located in concentric annuli. This system has a very rich phase diagram with at least four different phases. The layer in contact with the pore is always solid. For our narrow pore radius $(R=13\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$, as the density is increased, solidification takes place layer by layer, starting from the pore wall, as is confirmed by the static structure factors. The pore radius is too small to allow a bulklike solid to nucleate in the liquid region at the center of the pore, and in order to have a complete crystalline order in all the layers a pressure greater than $200\phantom{\rule{0.3em}{0ex}}\text{bar}$ is needed. Computing the one body density matrix we are able to estimate the condensate fraction, which is still nonzero even if all the layers are in the solid phase.