Fermion Cooper Pairing with Unequal Masses: Standard Field Theory Approach

TL;DR

This paper investigates fermion Cooper pairing with unequal masses using a standard field theory approach, revealing new insights into superfluid density, Meissner mass, and LOFF states, with implications for superfluidity and superconductivity.

Contribution

It derives superfluid density and Meissner mass relations for unequal mass fermions, showing breakdown of proportionality and establishing conditions favoring LOFF states.

Findings

Superfluid density is negative in weak coupling.

Meissner mass squared becomes positive with large mass ratios.

LOFF state is energetically favored due to negative superfluid density.

Abstract

The fermion Cooper pairing with unequal masses is investigated in a standard field theory approach. We derived the superfluid density and Meissner mass squared of the U(1) gauge field in a general two species model and found that the often used proportional relation between the two quantities is broken down when the fermion masses are unequal. In weak coupling region, the superfluid density is always negative but the Meissner mass squared becomes mostly positive when the mass ratio between the pairing fermions is large enough. We established a proper momentum configuration of the LOFF pairing with unequal masses and showed that the LOFF state is energetically favored due to the negative superfluid density. The single plane wave LOFF state is physically equivalent to an anisotropic state with a spontaneously generated superflow. The extension to finite range interaction is briefly discussed.