Two-dimensional fermionic superfluids, pairing instability and vortex liquids in the absence of time reversal symmetry

TL;DR

This paper investigates two-dimensional fermionic systems without time-reversal symmetry, revealing complex phase transitions including superfluid, insulator, and vortex liquid states, with implications for cold atom systems and high-temperature superconductors.

Contribution

It provides a detailed analysis of pairing instabilities and phase transitions, showing that a normal vortex-liquid phase preempts the superfluid-insulator transition in such systems.

Findings

Superfluid-insulator transition is second order in type-II systems.

A vortex-liquid normal phase emerges, preempting the pairing quantum phase transition.

Implications for cold atom systems and high-temperature superconductors.

Abstract

We consider a generic two-dimensional system of fermionic particles with attractive interactions and no disorder. If time-reversal symmetry is absent, it is possible to obtain incompressible insulating states in addition to the superfluid at zero temperature. The superfluid-insulator phase transition is found to be second order in type-II systems using a perturbative analysis of Cooper pairing instability in quantum Hall states of unpaired fermions. We obtain the pairing phase diagram as a function of chemical potential (density) and temperature. However, a more careful analysis presented here reveals that the pairing quantum phase transition is always preempted by another transition into a strongly correlated normal state which retains Cooper pairing and cannot be smoothly connected to the quantum Hall state of unpaired fermions. Such a normal phase can be qualitatively viewed as a liquid of vortices, although it may acquire conventional broken symmetries. Even if it did not survive at finite temperatures its influence would be felt through strong quantum fluctuations below a crossover temperature scale. These conclusions directly apply to fermionic ultra-cold atom systems near unitarity, but are likely relevant for the properties of other strongly correlated superfluids as well, including high temperature superconductors.