Dependence of interface conductivity on relevant physical parameters in polarized Fermi mixtures

TL;DR

This study investigates how the heat conductivity at the interface of polarized Fermi mixtures depends on physical parameters like temperature, mass ratio, and interaction strength, revealing a temperature threshold where conductivity drops.

Contribution

It provides a detailed numerical analysis of the heat conductivity dependence on multiple parameters in polarized Fermi systems, including the effects of mass asymmetry and interaction strength.

Findings

Interface conductivity drops at a temperature where particles' kinetic energy overcomes the superfluid gap.

The temperature $T_m$ for conductivity drop depends on mass ratio and interaction strength.

Range of relevant temperatures increases with larger mass ratios, especially for $^6$Li-$^{40}$K$ mixtures.

Abstract

We consider a mass-asymmetric polarized Fermi system in the presence of Hartree-Fock (HF) potentials. We concentrate on the BCS regime with various interaction strengths and numerically obtain the allowed values of the chemical and HF potentials, as well as the mass ratio. The functional dependence of the heat conductivity of the N-SF interface on relevant physical parameters, namely the temperature, the mass ratio, and the interaction strength, is obtained. In particular, we show that the interface conductivity starts to drop with decreasing temperature at the temperature, $T_{\text{m}}$, where the mean kinetic energy of the particles is just sufficient to overcome the SF gap. We obtain $T_{\text{m}}$ as a function of the mass ratio and the interaction strength. The variation of the heat conductivity, at fixed temperature, with the HF potentials and the imbalance chemical potential is also obtained. Finally, because the range of relevant temperatures increases for larger values of the mass ratio, we consider the $^6\text{Li}$-$^{40}\text{K}$ mixture separately by taking the temperature dependence of the pair potential into account.