Supersolid-like Behavior in Thin Solid $^4$He Films Adsorbed on a Nanoporous Glass

Two-dimensional $^4$He solid is a prospective system for observing supersolidity. We study thin solid $^4$He films adsorbed on a porous glass with 2.5 nm pore size. Torsional oscillator (TO) measurements are carried out for coverage $n$ from 6 to 30 $\mu$mol/m$^2$. Even in the solid films ($n < 21 \mu$mol/m$^2$) we have observed an increase in the TO frequency associated with a dissipation peak; i.e. the supersolid - like behavior. The onset temperature of the frequency shift shows an interesting coverage dependence: It is 1 K at 6 $\mu$mol/m$^2$ and approaches 0 K near the critical coverage $n_c = 21 \mu$mol/m$^2$, above which liquid film superfluidity is observed. The overall behaviors might be interpreted as a quantum critical phenomenon around $n_c$. Further studies including oscillation velocity dependence and measurements for solid $^3$He films are underway.