Supersolid Behavior in Confined Geometry

We have carried out torsional oscillator and heat capacity measurements on solid ${}^4\mathrm{He}$ samples grown within a geometry which restricts the helium to thin ($150\mu \mathrm{m}$) cylindrical disks. In contrast with previously reported values from Rittner and Reppy of 20% nonclassical rotational inertia for similar confining dimensions, 0.9% nonclassical rotational inertia (consistent with that found in bulk samples and samples embedded in porous media) was observed in our torsional oscillator cell. In this confined geometry, the heat capacity peak is consistent with that found in bulk solid samples of high crystalline quality.

Figure 1

NCRI and dissipation data for a 40 bar solid (sample $A$). The oscillator and thin disks creating the confined geometry are made of Be-Cu. The solid helium sample is composed of a stack of 19 thin annular disks (each with an outside/inside diameter and a thickness of 12.5 mm, 6.1 mm, and $150\mu \mathrm{m}$, respectively). The empty cell resonant period of this oscillator is 1.350 575 ms. Filling the cell with a 40 bar sample increases the period by 1240 ns.

Figure 2

NCRI data for four solid samples. Samples $A$, $B$, and $C$ are blocked capillary samples grown in $\sim 1\mathrm{h}$ with melting pressures of 40, 45, and 39 bar, respectively. Sample $C$ was then thermal cycled over the course of 3 h. Sample $D$ (a 37 bar solid) was grown as quickly as possible, solidifying in 15 minutes. All data are cooling scans at low drive ($\sim 10\mu \mathrm{m}/\mathrm{s}$).

Figure 3

Top panel (a) shows the heat capacity data for samples with different growth times for two different calorimeters. The open cell data are taken from Refs. 4, 27. (b) shows the specific heat peak as a function of temperature with the phonon $T^3$ term subtracted (please note that the scales are different for the two panels). The pressures for these samples are $33\pm 1\mathrm{bar}$. The solid helium sample consists of a stack of 24 solid helium disks with a thickness of $150\mu \mathrm{m}$ and diameter of 15 mm. The volume of the cell is 0.71 cc.

Figure 4

NCRI increases with the QF (i.e., faster solidification time). The circled outliers on the right are the two AgCu cells (as explained in the text), and the one on the left is the square cell from RR [10].