Pressure-Driven Flow of Solid Helium

The recent torsional oscillator results of Kim and Chan show an anomalous mass decoupling, interpreted by the authors as a supersolid phase transition, in solid ${}^4\mathrm{He}$. We have used a piezoelectrically driven diaphragm to study the flow of solid helium through an array of capillaries. Our measurements showed no indication of low temperature flow, placing stringent restrictions on supersolid flow in response to a pressure difference. The average flow speed at low temperatures was less than $1.2\times {10}^{-14}\mathrm{m}/\mathrm{s}$, corresponding to a supersolid velocity at least 7 orders of magnitude smaller than the critical velocities inferred from the torsional oscillator measurements.

Figure 1

Pressure response to “squeezes.” Lower curve (solid circles): liquid ${}^4\mathrm{He}$ at 1.95 K, 36.4 bar. Middle curve (open squares): solid ${}^4\mathrm{He}$ at 500 mK, 36.6 bar. Upper curve (open circles): solid ${}^4\mathrm{He}$ near melting at 1.95 K, 37.1 bar. Lines are guides to the eye. Note the different pressure axes.

Figure 2

Solid ${}^4\mathrm{He}$ response at 500 mK (upper curve, open symbols) and 35 mK (lower curve, solid symbols). Lines are guides to the eye and the curves are offset for clarity. Note the time scale, which is much longer than in Fig. 1.

Figure 3

ac pressure response in solid ${}^4\mathrm{He}$ at low temperatures. Solid symbols are taken at 0.1 Hz during cooling. Open squares at 35 and 500 mK were taken at 0.01 Hz.