Superfluid pairing between fermions with unequal masses

TL;DR

This paper develops a perturbation theory for superfluid fermionic gases with unequal masses, revealing how large mass differences affect critical temperature predictions and showing the universality of the results despite Efimov states.

Contribution

It extends BCS theory to account for large mass ratios, including second- and third-order effects, and demonstrates the universality of superfluid properties despite three-body resonances.

Findings

Critical temperature and order parameter differ from simple BCS predictions for large mass ratios.

The small parameter for perturbation theory is modified by the mass ratio, affecting density and scattering length requirements.

Three-body Efimov states do not influence the superfluid properties, indicating universality.

Abstract

We consider a superfluid state in a two-component gas of fermionic atoms with equal densities and unequal masses in the BCS limit. We develop a perturbation theory along the lines proposed by Gorkov and Melik-Barkhudarov and find that for a large difference in the masses of heavy ($M$) and light ($m$) atoms one has to take into account both the second-order and third-order contributions. The result for the critical temperature and order parameter is then quite different from the prediction of the simple BCS approach. Moreover, the small parameter of the theory turns out to be $(p_{F}|a|)/\hbar)\sqrt{M/m}\ll1$, where $p_{F}$ is the Fermi momentum, and $a$ the scattering length. Thus, for a large mass ratio $M/m$ the conventional perturbation theory requires significantly smaller Fermi momenta (densities) or scattering lengths than in the case of $M\sim m$, where the small parameter is $(p_{F}|a|)/\hbar)\ll1$. We show that 3-body scattering resonances appearing at a large mass ratio due to the presence of 3-body bound Efimov states do not influence the result, which in this sense becomes universal.