Disorder and the Supersolid State of Solid ${}^4\mathrm{He}$

We report torsional oscillator supersolid studies of highly disordered samples of solid ${}^4\mathrm{He}$. In an attempt to approach the amorphous or glassy state of the solid, we prepare our samples by rapid freezing from the normal phase of liquid ${}^4\mathrm{He}$. Less than two minutes is required for the entire process of freezing and the subsequent cooling of the sample to below 1 K. The supersolid signals observed for such samples are remarkably large, exceeding 20% of the entire solid helium moment of inertia. These results, taken with the finding that the magnitude of the small supersolid signals observed in our earlier experiments can be reduced to an unobservable level by annealing, strongly suggest that the supersolid state exists for the disordered or glassy state of helium and is absent in high quality crystals of solid ${}^4\mathrm{He}$.

Figure 1

Torsional oscillator: The motion of the torsion bob is excited and detected electrostatically. A Straty-Adams capacitance gauge, a heater, and a thermometer are attached on top of the torsion bob. At 4 K, the resonance frequency with the biggest insert is 874 Hz, and the mechanical quality factor is $Q=5\times {10}^5$.

Figure 2

Period and dissipation are shown as a function of temperature for the annular cell with 0.15 mm width. The first sample (open circles) was cooled to below 1 K over a period of three hours. Following this low temperature run, the sample was rapidly melted and quench-cooled (solid circles) to below 1 K in 90 s. The sample pressures were 41 (open circles) and 51 bar (solid circles), and the rim velocities at 300 mK were 9.7 (open circles) and $5.9\mu \mathrm{m}/\mathrm{s}$ (solid circles), respectively. The value of $P^{*}$ for both samples is 1.144 785 ms.

Figure 3

Pressure and period are shown as a function of time during annealing. The temperature is set to 1.57 K; the melting temperature of the sample is 2.35 K.

Figure 4

Period and dissipation are shown as a function of temperature in a cylindrical cell with a volume of $1.8{\mathrm{cm}}^3$. The sample (solid circles) was frozen and cooled below 1 K in 2 hours. The sample pressure was 32 bar, and the rim velocity at 300 mK was $24.7\mu \mathrm{m}/\mathrm{s}$. At a velocity of $9\mu \mathrm{m}/\mathrm{s}$, the graphs are identical. We also display the empty cell period and dissipation (open circles). The values of $P^{*}$ are 1.054 064 (solid circles) and 1.052 100 ms (empty cell).

Figure 5

Overview for a range of supersolid fractions as a function of surface to volume ratios from different researchers. All of the data obtained by the blocked capillary method are above 31 bar in order to avoid complications by the bcc phase. Cornell (solid circles); Penn State, annular cell (open circles) [2, 6], cylindrical cell $T_{\mathrm{melting}}=2.17\mathrm{K}$ (open triangle) [17], and cylindrical cell constant pressure growth 26 bar (open square) [17]; Shirahama et al. 41 bar (closed triangle) [3]. An upper bound on the size of the supersolid signal set by our earlier measurements in a square cell at 32 bar [5] is displayed as an inverted closed triangle.