Superfluidity of ${}^4\mathrm{He}$ nanoclusters in confinement

The structure and superfluid response of nanoscale size ${}^4\mathrm{He}$ clusters enclosed in spherical cavities are studied by computer simulations. The curved surface causes the formation of well-defined concentric shells, thus imparting to the system a very different structure from that of freestanding clusters. On a strongly attractive substrate, superfluidity is only observed at a low density, in the single layer coating the inner surface of the cavity. If the substrate is very weak (e.g., Li), on the other hand, a superfluid two-shell structure can form, whose physical properties interpolate between two and three dimensions. It is shown how experimental signatures of this physical behavior can be detected through measurements of the momentum distribution.

Figure 1

Energy per ${}^4\mathrm{He}$ atom $e$ (in K) versus number $N$ in the $T\to 0$ limit, inside Li (top) and glass (bottom) cavities of radius 10 Å. Dashed lines are polynomial fits to the data. Statistical errors are atmost equal to the symbol size.

Figure 2

Radial density profiles at $T=1$ K for a cluster of 25 ${}^4\mathrm{He}$ atoms inside a Li cavity (squares) and for 35 ${}^4\mathrm{He}$ atoms inside a glass cavity (circles). The origin is at the center of the cavity. Statistical errors are at most equal to the symbol size.

Figure 3

Radial density profiles at $T=1$ K for a cluster of 45 ${}^4\mathrm{He}$ atoms inside a Li cavity (squares) and a glass cavity (circles). The origin is at the center of the cavity. Also shown is the result for a free ${}^4\mathrm{He}$ cluster (diamonds), computed with respect to its center of mass. Statistical errors are at most equal to the symbol size.

Figure 4

Superfluid fraction at $T=1$ K of clusters of varying numbers of ${}^4\mathrm{He}$ atoms enclosed inside a Li (squares) and a glass (circles) cavity of radius $R=10\AA$. Where not explicitly shown, statistical errors are at most equal to the symbol size.

Figure 5

Superfluid fraction ${\rho }_S\left(T\right)$ versus temperature for a cluster of $N=45 {}^4\mathrm{He}$ atoms enclosed inside a Li (squares) and a glass (circles) cavity of radius $R=10\AA$. Also shown is the result for a free ${}^4\mathrm{He}$ cluster (diamond), computed with respect to its center of mass. Where not explicitly shown, statistical errors are at most equal to the symbol size.

Figure 6

Spherically averaged momentum distribution $n\left(q\right)$ computed for a cluster of $N=45 {}^4\mathrm{He}$ atoms enclosed inside a Li (bottom) and a glass (top) cavity of radius $R=10\AA$. Dashed lines refer to data at temperature $T=2$ K; solid lines, at $T=0.5$ K.