Critical Flow and Dissipation in a Quasi-One-Dimensional Superfluid

TL;DR

This study investigates superfluid helium flow in nanopores, revealing a crossover to quasi-one-dimensional behavior characterized by suppressed pressure dependence, power-law temperature dependence, and decreasing critical velocities as pore size diminishes.

Contribution

The paper provides experimental evidence of superfluid flow behavior in nanopores approaching 1D, highlighting deviations from bulk superfluidity and the influence of channel size on critical phenomena.

Findings

Suppressed pressure dependence of superfluid velocity in nanopores

Power-law temperature dependence of superfluid velocity

Decreasing critical velocities with smaller pore radii

Abstract

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of $^{4}$He belongs to the same three dimensional $\mathrm{O}(2)$ universality class as the onset of ferromagnetism in a lattice of classical spins with $XY$ symmetry. Below the transition, the superfluid density $\rho_s$ and superfluid velocity $v_s$ increase as power laws of temperature described by a universal critical exponent constrained to be equal by scale invariance. As the dimensionality is reduced towards one dimension (1D), it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single $30~$nm long nanopores with radii ranging down from 20~nm to 3~nm. As the pore size is reduced towards the 1D limit, we observe: {\it i)} a suppression of the pressure dependence of the superfluid velocity; {\it ii)} a temperature dependence of $v_{s}$ that surprisingly can be well-fitted by a powerlaw with a single exponent over a broad range of temperatures; and {\it iii)} decreasing critical velocities as a function of radius for channel sizes below $R \simeq 20$~nm, in stark contrast with what is observed in micron sized channels. We interpret these deviations from bulk behaviour as signaling the crossover to a quasi-1D state whereby the size of a critical topological defect is cut off by the channel radius.