Universal collective modes in 2 dimensional chiral superfluids

TL;DR

This paper investigates collective modes in 2D chiral superfluids, revealing universal sub-gap modes for all angular momenta and linking them to Fermi liquid effects and instabilities.

Contribution

It extends known results to all chiral ground states with angular momentum L≥1, identifying universal sub-gap modes and their relation to Fermi liquid parameters and instabilities.

Findings

Existence of a sub-gap mode with mass √2 Δ for all L≥1

Mode mass renormalization linked to Landau parameters

Modes become massless at Pomeranchuk instability

Abstract

In this work, we utilize semi-classical kinetic equations to investigate the order parameter collective modes of a class of 2 dimensional superfluids. Extending the known results for $p$-wave superfluids, we show for any chiral ground state of angular momentum $L\geq 1$, there exists a sub-gap mode with mass $\sqrt{2}\, \Delta$ in the BCS limit, where $\Delta$ is the magnitude of the ground state gap. We determine the most significant Landau parameter which contributes to the mass renormalization and show explicitly the renormalized modes become massless at the Pomeranchuk instability of the fermion vacuum. Particularly for $L=1$, we propose a continuous field theory to include the Fermi liquid effect in quadrupolar channel and produce the same result under consistent approximations. They provide potential diagnostics for distinguishing 2 dimensional chiral ground states of different angular momenta with order parameter collective modes and reveal another low energy degrees of freedom near nematic transition.