Structure, superfluidity, and quantum melting of hydrogen clusters

Abstract

We present results of a theoretical study of para-${\mathrm{H}}_{2}$ $(p\text{\ensuremath{-}}{\mathrm{H}}_{2})$ and ortho-${\mathrm{D}}_{2}$ $(o\text{\ensuremath{-}}{\mathrm{D}}_{2})$ clusters at low temperature $(0.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}\ensuremath{\leqslant}T\ensuremath{\leqslant}3.5\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ based on path integral Monte Carlo simulations. Clusters of $N\ensuremath{\leqslant}21$ $p\text{\ensuremath{-}}{\mathrm{H}}_{2}$ molecules are nearly entirely superfluid at $T\ensuremath{\leqslant}1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. For $22\ensuremath{\leqslant}N\ensuremath{\leqslant}30$, the superfluid response displays strong variations with $N$, reflecting structural changes that occur on adding or removing even a single molecule. Some clusters in this size range display quantum melting, going from solidlike to liquidlike as $T\ensuremath{\rightarrow}0$. Melting is caused by quantum exchanges of molecules. The largest $p\text{\ensuremath{-}}{\mathrm{H}}_{2}$ cluster for which a significant superfluid response is observed comprises $N=27\phantom{\rule{0.3em}{0ex}}\text{molecules}$. Evidence of a finite superfluid response is presented for $o\text{\ensuremath{-}}{\mathrm{D}}_{2}$ clusters of size up to $N=14$. Magic numbers are observed, at which both types of clusters feature pronounced stability.