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arXiv:2607.28335 · Physical review. B./Physical review. B

Fulde-Ferrell-Larkin-Ovchinnikov transition and quantum criticality in polarized Fermi gases

Francesco Pirolo, L. Pisani, P. Pieri

Published Oct 26, 2026• 0 citations
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Abstract

We investigate the zero-temperature transition from the polarized normal phase to the FFLO state in a two-dimensional Fermi gas by means of a diagrammatic t-matrix approach. We first show that the standard non-self-consistent theory produces an unphysical phase diagram because of a severe violation of the Luttinger theorem. Motivated by this observation, we introduce a minimal self- consistent extension that largely restores compliance with the Luttinger theorem while preserving the analytical simplicity of the original formalism. This leads to a physically consistent phase diagram over the whole interaction range. Building on this improved description, we characterize the quantum critical behavior of the FFLO transition through the quasiparticle decay rates, quasiparticle weights, momentum distributions, and the critical dynamics of both fermionic and bosonic degrees of freedom. We further compare the two- and three-dimensional systems, showing that their critical properties can be understood within a unified geometrical picture based on the nesting of the majority and minority Fermi surfaces. Finally, for the three-dimensional case, we demonstrate within the Hertz-Millis framework that vertex corrections are irrelevant, thereby placing the FFLO quantum phase transition in the mean-field universality class, in close analogy with itinerant antiferromagnets.

DOI
10.1103/4wwz-xg5q

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We investigate the zero-temperature transition from the polarized normal phase to the FFLO state in a two-dimensional Fermi gas by means of a diagrammatic t-matrix approach. We first show that the standard non-self-consistent theory produces an unphysical phase diagram because of a severe violation of the Luttinger theorem. Motivated by this observation, we introduce a minimal self- consistent extension that largely restores compliance with the Luttinger theorem while preserving the analytical simplicity of the original formalism. This leads to a physically consistent phase diagram over the whole interaction range. Building on this improved description, we characterize the quantum critical behavior of the FFLO transition through the quasiparticle decay rates, quasiparticle weights, momentum distributions, and the critical dynamics of both fermionic and bosonic degrees of freedom. We further compare the two- and three-dimensional systems, showing that their critical properties can be understood within a unified geometrical picture based on the nesting of the majority and minority Fermi surfaces. Finally, for the three-dimensional case, we demonstrate within the Hertz-Millis framework that vertex corrections are irrelevant, thereby placing the FFLO quantum phase transition in the mean-field universality class, in close analogy with itinerant antiferromagnets.
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 ttt-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 interparticle 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 quasiparticle 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, quasiparticles 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 quasiparticle residues vanish and the effective masses diverge. This behavior leads to a complete breakdown of the quasiparticle 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.
We calculate the zero-temperature (T=0) phase diagram of a polarized two-component Fermi gas in an array of weakly coupled parallel one-dimensional (1D) "tubes" produced by a two-dimensional optical lattice. Increasing the lattice strength drives a crossover from three-dimensional (3D) to 1D behavior, stabilizing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superfluid phase. We argue that the most promising regime for observing the FFLO phase is in the quasi-1D regime, where the atomic motion is largely 1D but there is weak tunneling in the other directions that stabilizes long-range order. In the FFLO phase, we describe a phase transition where the quasiparticle spectrum changes from gapless near the 3D regime to gapped in quasi-1D.
Motivated by the recent experimental realization of a candidate to the Fulde-Ferrell (FF) and the Larkin-Ovchinnikov (LO) states in one dimensional (1D) atomic Fermi gases, we study the quantum phase transitions in these enigmatic, finite momentum-paired superfluids. We focus on the FF state and investigate the effects of the induced interaction on the stability of the FFLO phase in homogeneous spin-imbalanced quasi-1D Fermi gases at zero temperature. When this is taken into account we find a direct transition from the fully polarized to the FFLO state. Also, we consider the effect of a finite lifetime of the quasi-particles states in the normal-superfluid instability. In the limit of long lifetimes, the lifetime effect is irrelevant and the transition is directly from the fully polarized to the FFLO state. We show, however, that for sufficiently short lifetimes there is a quantum critical point (QCP), at a finite value of the mismatch of the Fermi wave-vectors of the different quasi-particles, that we fully characterize. In this case the transition is from the FFLO phase to a normal partially polarized state with increasing mismatch.
We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov--de Gennes equations, as well as the exact Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired Bardeen-Cooper-Schrieffer (BCS) state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimensions. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure appears, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.
We calculate the pair susceptibility of an attractive spin-polarized Fermi gas in the normal phase, as a function of the pair momentum. Close to unitarity, we find a strong enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing fluctuations over an extended region of the temperature-polarization phase diagram, which manifests itself as a pronounced peak in the pair-momentum distribution at a finite pair momentum. This peak should be amenable to experimental observation at achievable temperatures in a boxlike trapping potential, as a fingerprint of FFLO pairing. Our calculations rest on a self-consistent ttt-matrix approach which, for the unitary balanced Fermi gas, has been validated against experimental data for several thermodynamic quantities.
We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair, and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.