A shell model for superfluids in rough-walled nanopores

TL;DR

This paper introduces a shell model of coupled Luttinger liquids to describe the crossover from localized to superfluid flow in helium-4 within nanopores, based on pore size and substrate effects.

Contribution

It proposes a novel shell model framework to explain superfluid behavior in nanopores, extending previous quantum Monte Carlo results.

Findings

Small radius pores localize helium atoms, preventing superfluidity.

Above a critical radius, a 1D superfluid channel emerges.

The model captures the crossover from localized to superfluid flow.

Abstract

Recent experiments on the flow of helium-4 fluid through nanopores with tunable pore radius provide a platform for studying the quasi-one-dimensional (quasi-1D) superfluid behaviors. In the extreme 1D limit, the helium atoms are localized by disordered small variations in the substrate potential provided by the pore walls. In the limit of wide pore radius, a solid layer of helium-4 is expected to coat the pore walls smoothing out the substrate potential, and superfluidity is observed in the central region. Building on earlier quantum Monte Carlo results, we propose a scenario for this crossover using a shell model of coupled Luttinger liquids. We find that a small radius pore will always localize the helium atoms, but above a critical radius, a single 1D channel flows through the pore and can be described by Luttinger liquid theory.