Fermion pairing in Bose-Fermi mixtures

TL;DR

This paper derives an effective interaction between fermions in a Bose-Fermi mixture, showing that fermion pairing and potential superconductivity can occur at ultra-cold temperatures, with a small energy gap relative to the Fermi energy.

Contribution

It introduces a self-consistent calculation of fermion pairing mediated by bosonic density fluctuations, considering multi-phonon contributions and simplifying assumptions about fermion velocities.

Findings

Superconducting phase can occur at temperatures > 100nK.

Energy gap is approximately 1% of the Fermi energy.

Effective interaction is induced by bosonic density fluctuations.

Abstract

An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-l channels. It has been found that the onset of the superconducting phase can occur at temperatures (> 100nK) of the same order of magnitude as the Fermi temperature (300nK), and the energy gap in the excitation spectrum is a small fraction (1%) of the Fermi energy.