Pairing instability driven by macroscopically degenerate collective modes in two-dimensional rotating fermion liquids near unitarity

TL;DR

This paper investigates the normal phases of two-dimensional rotating fermion liquids near unitarity, revealing macroscopically degenerate collective modes that influence the stability of superfluid states and lead to potential quantum Hall states of Cooper pairs.

Contribution

It introduces a model with SP(2N) symmetry to analyze the quantum critical region and demonstrates the existence of macroscopically degenerate bosonic modes in the normal phase.

Findings

Degenerate bosonic modes persist to all orders in 1/N.

Finite-range interactions lift degeneracy, promoting quantum melting of flux lattices.

Normal states may form quantum Hall states of Cooper pairs.

Abstract

Fermionic superfluids can undergo phase transitions into different kinds of normal regimes, loosely characterized by whether Cooper pairs remain locally stable. If the normal phase retains strong pairing fluctuations, it behaves like a liquid of vortices, which has been observed in cuprate superconductors. We argue that analogous strongly correlated normal states exist in two-dimensional neutral fermion liquids near unitarity, where superfluid is destroyed by fast rotation. These states have non-universal properties, and if they develop as distinct thermodynamic phases they can be characterized as quantum Hall states of Cooper pairs. The formal analysis is based on a model with SP(2N) symmetry that describes the quantum critical region in the vicinity of a broad Feshbach resonance. We explore the pairing phase diagram and demonstrate that the considered model has macroscopically degenerate bosonic modes in the normal phase, to all orders in 1/N. It takes finite-range interactions to lift this degeneracy, making the Abrikosov flux lattice of the superfluid particularly susceptible to quantum melting.