Phase-slip avalanches in the superflow of $^4$He through arrays of nanopores

TL;DR

This paper models phase-slip dynamics in superfluid helium-4 through nanopore arrays, revealing a disorder-driven transition between synchronized and avalanche-like phase-slippage regimes at low temperatures.

Contribution

It introduces a theoretical model incorporating disorder and inter-pore coupling to explain the transition from synchronous to asynchronous phase-slippage observed experimentally.

Findings

Identification of a phase transition between non-avalanching and avalanching regimes.

Prediction of how disorder broadens critical velocities at low temperatures.

Explanation of the loss of synchronicity in phase-slippage with decreasing temperature.

Abstract

Recent experiments by Sato et al. [1] have explored the dynamics of $^4$He superflow through an array of nanopores. These experiments have found that, as the temperature is lowered, phase-slippage in the pores changes its character, from synchronous to asynchronous. Inspired by these experiments, we construct a model to address the characteristics of phase-slippage in superflow through nanopore arrays. We focus on the low-temperature regime, in which the current-phase relation for a single pore is linear, and thermal fluctuations may be neglected. Our model incorporates two basic ingredients: (1) each pore has its own random value of critical velocity (due, e.g., to atomic-scale imperfections), and (2) an effective inter-pore coupling, mediated through the bulk superfluid. The inter-pore coupling tends to cause neighbours of a pore that has already phase-slipped also to phase-slip; this process may cascade, creating an avalanche of synchronously slipping phases. As the temperature is lowered, the distribution of critical velocities is expected to effectively broaden, owing to the reduction in the superfluid healing length, leading to a loss of synchronicity in phase-slippage. Furthermore, we find that competition between the strength of the disorder in the critical velocities and the strength of the inter-pore interaction leads to a phase transition between non-avalanching and avalanching regimes of phase-slippage. [1] Sato, Y., Hoskinson, E. Packard, R. E. cond-mat/0605660.