Dissipative superfluid mass flux through solid 4He

TL;DR

This study investigates superfluid helium flow through solid 4He, revealing dissipative, nonlinear behavior suggestive of Luttinger liquid characteristics, with flow likely occurring along dislocation cores.

Contribution

It provides detailed measurements of helium flow through solid 4He, demonstrating temperature-dependent dissipation and nonlinear flow behavior indicative of one-dimensional Luttinger liquid physics.

Findings

Flow decreases with increasing temperature above 100 mK.

Flow exhibits nonlinear dependence on chemical potential difference, with an exponent less than 0.5.

Flow behavior suggests superfluidity along dislocation cores in solid helium.

Abstract

The thermo-mechanical effect in superfluid helium is used to create an initial chemical potential difference, $\Delta \mu_0$, across a solid $^4$He sample. This $\Delta \mu_0$ causes a flow of helium atoms from one reservoir filled with superfluid helium, through a sample cell filled with solid helium, to another superfluid-filled reservoir until chemical potential equilibrium is restored. The solid helium sample is separated from each of the reservoirs by Vycor rods that allow only the superfluid component to flow. With an improved technique, measurements of the flow, $F$, at several fixed solid helium temperatures, $T$, have been made as function of $\Delta \mu$ in the pressure range 25.5 - 26.1 bar. And, measurements of $F$ have been made as a function of temperature in the range $180 < T < 545$~mK for several fixed values of $\Delta \mu$. The temperature dependence of the flow above $100$~mK shows a reduction of the flux with an increase in temperature that is well described by $F = F_0^*[1 - a\exp(-E/T)]$. The non-linear functional dependence $F \sim (\Delta \mu)^b$, with $b < 0.5$ independent of temperature but dependent on pressure, documents in some detail the dissipative nature of the flow and suggests that this system demonstrates Luttinger liquid-like one-dimensional behavior. The mechanism that causes this flow behavior is not certain, but is consistent with superflow on the cores of edge dislocations.