Evolution of an attractive polarized Fermi gas: From a Fermi liquid of polarons to a non-Fermi liquid at the Fulde-Ferrell-Larkin-Ovchinnikov quantum critical point

TL;DR

This paper investigates the evolution of an attractive polarized Fermi gas across the BCS-BEC crossover, revealing a transition from a Fermi liquid of polarons to a non-Fermi liquid at the FFLO quantum critical point, with implications for superfluid phases.

Contribution

It provides a self-consistent zero-temperature phase diagram across the BCS-BEC crossover, identifying conditions for FFLO and BCS superfluid instabilities and characterizing the breakdown of Fermi liquid behavior near the FFLO QCP.

Findings

Quasi-particles remain well-defined near BCS superfluid instability.

Near FFLO QCP, quasi-particle residues vanish and effective masses diverge.

Non-Fermi liquid behavior appears at finite temperature near the FFLO QCP.

Abstract

The evolution of an attractive polarized two-component Fermi gas at zero temperature is analyzed as its polarization is progressively decreased, from full polarization (corresponding to the polaronic limit) down to a critical polarization when superfluidity sets in. This critical polarization and the nature of the associated superfluid instability are determined within a fully self-consistent $t$-matrix approach implemented exactly at zero temperature. In this way, the polarization-vs-coupling phase diagram at zero temperature is constructed throughout the whole BCS-BEC crossover. Depending on the coupling strength of the inter-particle interaction between the two components, the superfluid instability can be either toward a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase or toward a standard polarized BCS phase. The evolution with polarization of the quasi-particle parameters in the normal Fermi gas turns out to be notably different in the two cases. When the instability is toward a polarized BCS superfluid, quasi-particles in the proximity of the two Fermi surfaces remain well defined for all polarizations. When the instability is instead toward an FFLO superfluid, precursor effects become apparent upon approaching the FFLO quantum critical point (QCP), where the quasi-particle residues vanish and the effective masses diverge. This behavior leads to a complete breakdown of the quasi-particle picture characteristic of a Fermi liquid, similarly to what occurs in heavy-fermion materials at an antiferromagnetic QCP. At unitarity, the system is further investigated at finite temperature, making it possible to identify a non-Fermi liquid region in the temperature-vs-polarization phase diagram associated with the underlying FFLO QCP.