Effect of Rough Walls on Transport in Mesoscopic $^3$He Films

TL;DR

This paper investigates how rough surfaces affect mesoscopic transport in superfluid helium-3 films, revealing the impact of boundary scattering on relaxation times and conductivity, with implications for electronic systems.

Contribution

It introduces a quasiclassical theory incorporating surface roughness spectra to explain transport anomalies in $^3$He films and suggests methods to enhance metallic film conductivity.

Findings

The theory explains the temperature dependence of relaxation rates.

Surface roughness significantly influences mass transport.

Results can inform improvements in metallic thin film conductivity.

Abstract

The interplay of bulk and boundary scattering is explored in a regime where quantum size effects modify mesoscopic transport in a degenerate Fermi liquid film of $^3$He on a rough surface. We discuss mass transport and the momentum relaxation time of the film in a torsional oscillator geometry within the framework of a quasiclassical theory that includes the experimentally determined power spectrum of the rough surface. The theory explains the anomalous temperature dependence of the relaxation rate observed experimentally. We model further studies on $^3$He confined in nanofluidic sample chambers with lithographically defined surface roughness. The improved understanding of surface roughness scattering can be extended to the analogous system of electrons in metals and suggests routes to improve the conductivity of thin metallic films.