Transport in thin polarized Fermi-liquid films

TL;DR

This paper provides low-temperature, polarization-dependent expressions for transport properties like thermal conductivity, shear viscosity, and spin diffusion in two-dimensional polarized Fermi-liquid films, with applications to extsuperscript{3}He films.

Contribution

It offers the first essentially exact low-temperature formulas for transport coefficients in polarized 2D Fermi liquids, including detailed density and polarization dependence predictions.

Findings

ext{Thermal conductivity} \, \kappa^{-1} \sim T \ln T

ext{Shear viscosity} \, \eta^{-1} \sim T^2

ext{Spin diffusion coefficient} \, D ext{ increases with polarization}

Abstract

We calculate expressions for the state-dependent quasiparticle lifetime, the thermal conductivity $\kappa$, the shear viscosity $\eta$, and discuss the spin diffusion coefficient $D$ for Fermi-liquid films in two dimensions. The expressions are valid for low temperatures and arbitrary polarization. The low-temperature expressions for the transport coefficients are essentially exact. We find that $\kappa^{-1} \sim T \ln{T}$, and $\eta^{-1} \sim T^{2}$ for arbitrary polarizations $0 \le {\mathcal{P}} \le 1$. We note that the shear viscosity requires a unique analysis. We utilize previously determined values for the density and polarization dependent Landau parameters to calculate the transition probabilities in the lowest order "$\ell = 0$ approximation," and thus we obtain predictions for the density, temperature and polarization dependence of the thermal conductivity, shear viscosity, and spin diffusion coefficient for thin \he3 films. Results are shown for second layer \he3 films on graphite, and thin \he3-\he4 superfluid mixtures. The density dependence is discussed in detail. For $\kappa$ and $\eta$ we find roughly an order of magnitude increase in magnitude from zero to full polarization. For $D$ a simialr large increase is predicted from zero polarization to the polarization where $D$ is a maximum ($\sim 0.74$). We discuss the applicability of \he3 thin films to the question of the existence of a universal lower bound for the ratio of the shear viscosity to the entropy density.