Pairing from repulsion in a two-dimensional Fermi gas with soft-core interactions

TL;DR

This paper uses numerical FRG to explore how repulsive soft-core interactions in a 2D Fermi gas lead to unconventional superfluid states with higher angular momentum pairing, revealing new pathways for superfluidity beyond traditional mechanisms.

Contribution

It demonstrates that tuning the interaction potential shape can stabilize higher angular momentum superfluid phases, extending understanding beyond the original Kohn-Luttinger theory.

Findings

Higher angular momentum pairing states like f- and h-wave are stabilized by repulsive soft-core interactions.

FRG predicts phase boundaries more accurately than second-order perturbative calculations.

Tuning interaction shape enhances pairing strength and enables nontrivial superfluid phases.

Abstract

We investigate a model many-body system of spinless Fermi gas in two dimensions, where the bare two-body interaction is repulsive and takes the form of a soft-core disk potential. We obtain the zero temperature phase diagram of this model by numerical functional renormalization group (FRG), which retains the effective interaction vertices in all channels to provide a detailed picture of how Cooper pairing emerges under the renormalization flow. The repulsion drives the system to a series of superfluid states with higher angular momentum paring, for example in the $f$- and $h$-wave channels instead of the $p$-wave channel. This is in sharp contrast to the original Kohn-Luttinger mechanism where pairing of very large angular momenta and exponentially small transition temperature was predicted. We trace the stabilization and enhancement of $f$- and $h$-wave pairing back to the momentum dependence of the bare interaction. A perturbative calculation is carried out to show that while the second order Kohn-Luttinger diagrams provide a qualitative understanding of the onsets of the various superfluid phases, they are unable to accurately capture the phase boundaries predicted by FRG. Our findings suggest that tuning the shape of the interaction potential offers a promising route to achieve stronger ``pairing glue" and to realize nontrivial superfluid phases in repulsive Fermi gases beyond the scope of the original Kohn-Luttinger analysis.