Superfluidlike Mass Flow Through $8\mu \mathrm{m}$ Thick Solid ${}^4\mathrm{He}$ Samples

We report the observation of superfluidlike mass flow through coin-shaped $8\mu \mathrm{m}$ thick solid ${}^4\mathrm{He}$ samples sandwiched between superfluid leads. Mass flow is found from the melting pressure to at least 30 bar with a concomitant decrease in the onset temperature from 1 to 0.25 K. The mass-flow rate is found to be sample dependent and can be enhanced by thermal annealing. The flow rate decreases with temperature and decays nearly exponentially with the pressure of the samples. The dissipation associated with the mass flow decreases with temperature and becomes superfluidlike near 0.1 K. In contrast to earlier studies on centimeter-thick samples, we do not see a sharp cutoff in the mass-flow rate at low temperature.

Figure 1

Boundary of the mass flow phenomenon in solid ${}^4\mathrm{He}$. Mass flow is found to the left of the dashed blue curve defined by $T_{\text{onset}}$, the onset temperatures extrapolated from mass flow vs temperature data from Fig. 4. The blue dashed curve is a simple exponential fitting of the $T_{\text{onset}}$ data. Inset: Schematic drawing of the sample cell.

Figure 2

Time evolution of $PR$ and $PL$ in response to (a) the injection of ${}^4\mathrm{He}$ gas to the left of the sample cell at $t=19\mathrm{s}$ and (b) the introduction (at $t=425\mathrm{s}$) and removal (at $t=605\mathrm{s}$) of a 20-mK heat pulse on $SL$. Flow rates shown in panels (a) and (b) are identical at $0.23\mathrm{mbar}/\mathrm{s}$. (c) The exponential approach of $PL$ towards a constant $PR$ indicates the mass flow is limited by the normal fluid inside Vycor. (d) $PL$ and $PR$ equilibrate towards each other after an injection of ${}^4\mathrm{He}$ gas to the right side of a 30.1-bar sample. The mass-flow rate decreases with temperature between 0.1 to 0.25 K. There is no evidence of flow above 0.3 K. Pressure oscillations came from oscillations of the still temperature.

Figure 3

Responses of the change in $PR$ ($\mathrm{\Delta }PR$) vs time ($t$) of sample $\mathrm{S}505$ at 0.1, 0.2, 0.3, and 0.4 K immediately after the removal of heat pulse. Equilibrium is reached at $t=\tau$ when $PR=PL$. The red dashed straight lines highlight the onset of curvature in $PR$ vs time that appears above 0.1 K.

Figure 4

Mass-flow rate vs temperature of solid samples at different pressures. Normalized mass-flow rates (flow rate at 0.1 K $=1$) of the $\mathrm{T}\mathrm{S}$ and $\mathrm{T}\mathrm{H}$ samples are shown in the inset. The result from a UM sample at 26.4 bar [4] is shown in the inset as a dashed curve.

Figure 5

Mass-flow rate measured at 0.1 K as a function of sample pressure. The flow rate of superfluid through the Vycor cylinders at 450 ng/s is marked by a blue horizontal dashed line (see Sec. III of the Supplemental Material [12]). This sets the upper limit of the observed flow rate. When the data at and near this saturated value are excluded, the flow rates of all nine sequences of samples show nearly exponential decay with pressure. Decay constants and flow rates show sample-to-sample variation. The Vycor bottleneck effect prevents the measurement of the flow rate of samples between 27.3 and 29.5 bar. The red dashed-dotted curve represents a quadratic dependence of the flow rate on pressure $P[\text{rate}=A_0(P-P_m{)}^{-2}+B_0]$. $P_m$ is the melting pressure and $A_0$ and $B_0$ are constants determined by anchoring the curve at two data points of the $SA$ sequence. Such a quadratic dependence is predicted if liquid channels are responsible for the mass flow [20, 21].