Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

BREAKING TRANSLATIONAL INVARIANCE BY POPULATION IMBALANCE: THE FULDE–FERRELL–LARKIN–OVCHINNIKOV STATES

Gertrud Zwicknagl, Jochen Wosnitza

Published Aug 30, 2010• 38 citations
Publisher

Abstract

An overview is given of our present understanding of superconductivity with spontaneously broken translation symmetry in polarized Fermi systems. The existence of "crystalline" superconducting phases is considered in a wide range of systems, prominent examples being conduction electrons in metals, ultra-cold atoms in a trap, nuclear matter and dense quark systems. The underlying physics is delineated and theoretical approaches to the inhomogeneous phases and their properties are discussed. From the experimental side, it is argued that superconductivity with imbalance-induced order parameters is realized in layered organic compounds and potentially in heavy-fermion systems.

DOI
10.1142/s0217979210056396

Related papers

Realization, Characterization, and Detection of Novel Superfluid Phases with Pairing between Unbalanced Fermion Species

Kun Yang

In this chapter we review recent experimental and theoretical work on various novel superfluid phases in fermion systems, that result from pairing fermions of different species with unequal densities. After briefly reviewing existing experimental work in superconductors subject to a strong magnetic field and trapped cold fermionic atom systems, we discuss how to characterize the possible pairing phases based on their symmetry properties, and the structure/topology of the Fermi surface(s) formed by the unpaired fermions due to the density imbalance. We also discuss possible experimental probes that can be used to directly detect the structure of the superfluid order parameter in superconductors and trapped cold atom systems, which may establish the presence of some of these phases unambiguously.

arXiv:cond-mat/0603190•Series on advances in quantum many-body theory•Nov 1, 2006•3 citations

Imbalanced Fermi systems and exotic superconducting phases

Madhuparna Karmakar

Quantum many body phases, in competition or coexistence has always been a fascinating area of research in condensed matter physics. One of the most widely investigated scenario of phase competition is that between superconductivity and magnetism, which in spite of several decades of research continues to bring up new surprises till date. While superconductivity and magnetism are naively considered to be antagonists, there are several circumstances where these many body phases can be found to be cooperating, coexisting and even promoting each other. The results of such cooperative behavior are found to show up as exotic quantum phases. In this chapter we discuss about such an exotic superconducting phase, which comes to life when a particular class of superconducting material viz. "Pauli limited superconductors" are subjected to an imbalance between the population of the fermionic species undergoing pairing. The consequence of such an imbalance is the emergence of a non-trivial spatially modulated superconducting phase, popularly known as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Characterized by a finite momentum pairing between the fermionic species the FFLO phase hosts a non zero magnetization, leading to an unconventional coexistent phase of superconductivity and magnetism.

arXiv:2008.11740•Aug 26, 2020•0 citations

Larkin-Ovchinnikov superfluidity in a two-dimensional imbalanced atomic Fermi gas

Umberto Toniolo, Brendan C. Mulkerin, Xia-Ji Liu +1 more

We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with explicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. To systematically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen-Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas (${N}_{\text{PP}}$). The order of the phase transitions has been examined and, in particular, we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.

arXiv:1609.06692•Physical Review A•Jan 4, 2017•14 citations

Exotic Superfluid Phases in Spin-Polarized Fermi Gases in Optical Lattices

Ettore Vitali, Peter Rosenberg, Shiwei Zhang

Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly 500 atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between spin imbalance, strong interactions, and superfluidity in an exotic phase of matter.

arXiv:2110.06159•Physical Review Letters•May 17, 2022•16 citations

Condensation and pairing in inhomogeneous cold atomic and electronic systems

Kuei Sun

This thesis presents a theoretical study of Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) pairing states in inhomogeneous systems of cold atoms and of electrons. Features of spatially separated phases are explored, with particular focus on the behavior of the condensed phase and its experimental measures. Three specific systems are addressed below. First, we study bosonic atoms in three-dimensional optical lattices in the presence of an external spherical harmonic trapping potential. We investigate the critical value associated with the lattice depth and interaction strength below which the system undergoes a quantum phase transition from a global BEC phase to a coexistence of local BEC and Mott-insulating phases. We discuss the ground state properties, excitations, and experimental signatures of the condensate surrounded by the Mott-insulators. BCS pairing in fermionic atoms of two spin species that are confined to spatially separated trapping potentials is investigated next. We investigate the one-dimensional limit and find that, with increasing separation between the spin-dependent traps, the fermions undergo a transition from a global fully-paired phase to a coexistence of a fully-paired phase, a spin-imbalanced phase with oscillatory pairing, the so-called Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, and an unpaired completely spin-polarized phase. We present numerical profiles of key parameters of the phase diagram as well as observable signatures of the oscillatory pairing phase. The third topic is that of transport physics in a superconductor-ferromagnetic-metal (S/F) hybrid in which superconducting phases and ferromagnetic normal phases are artificially combined. We model the interface between the S and F regions and discuss possible scattering processes at the interface. We apply the Blonder-Tinkham-Klapwijk treatment with the interfacial model to calculate resistance of the system. These results explain recent experimental observations.

•Jan 1, 2011•0 citations

Surface Pair-Density-Wave Superconducting and Superfluid States

Mats Barkman, Albert Samoilenka, Egor S. Babaev

Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous superconducting and superfluid ground states, spontaneously breaking translation symmetries. In this Letter, we demonstrate that the transition from the FFLO to the normal state as a function of temperature or increased Fermi surface splitting is not a direct one. Instead, the system has an additional phase transition to a different state where pair-density-wave superconductivity (or superfluidity) exists only on the boundaries of the system, while the bulk of the system is normal. The surface pair-density-wave state is very robust and exists for much larger fields and temperatures than the FFLO state.

arXiv:1811.09590•Physical Review Letters•Apr 25, 2019•18 citations
An overview is given of our present understanding of superconductivity with spontaneously broken translation symmetry in polarized Fermi systems. The existence of "crystalline" superconducting phases is considered in a wide range of systems, prominent examples being conduction electrons in metals, ultra-cold atoms in a trap, nuclear matter and dense quark systems. The underlying physics is delineated and theoretical approaches to the inhomogeneous phases and their properties are discussed. From the experimental side, it is argued that superconductivity with imbalance-induced order parameters is realized in layered organic compounds and potentially in heavy-fermion systems.
In this chapter we review recent experimental and theoretical work on various novel superfluid phases in fermion systems, that result from pairing fermions of different species with unequal densities. After briefly reviewing existing experimental work in superconductors subject to a strong magnetic field and trapped cold fermionic atom systems, we discuss how to characterize the possible pairing phases based on their symmetry properties, and the structure/topology of the Fermi surface(s) formed by the unpaired fermions due to the density imbalance. We also discuss possible experimental probes that can be used to directly detect the structure of the superfluid order parameter in superconductors and trapped cold atom systems, which may establish the presence of some of these phases unambiguously.
Quantum many body phases, in competition or coexistence has always been a fascinating area of research in condensed matter physics. One of the most widely investigated scenario of phase competition is that between superconductivity and magnetism, which in spite of several decades of research continues to bring up new surprises till date. While superconductivity and magnetism are naively considered to be antagonists, there are several circumstances where these many body phases can be found to be cooperating, coexisting and even promoting each other. The results of such cooperative behavior are found to show up as exotic quantum phases. In this chapter we discuss about such an exotic superconducting phase, which comes to life when a particular class of superconducting material viz. "Pauli limited superconductors" are subjected to an imbalance between the population of the fermionic species undergoing pairing. The consequence of such an imbalance is the emergence of a non-trivial spatially modulated superconducting phase, popularly known as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Characterized by a finite momentum pairing between the fermionic species the FFLO phase hosts a non zero magnetization, leading to an unconventional coexistent phase of superconductivity and magnetism.
We present an extensive study of two-dimensional Larkin-Ovchinnikov (LO) superfluidity in a spin-imbalanced two-component atomic Fermi gas. In the context of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, we explore a wide and generic class of pairing gap functions with explicit spatial dependency. The mean-field theory of such phases is applied through the Bogoliubov-de Gennes equations in which the pairing gap can be determined self-consistently. To systematically explore the configuration space we consider both the canonical and grand canonical ensembles where we control the polarization or chemical potentials of the system, respectively. The mean-field calculations enable us to understand the nature of the phase transitions in the fully paired Bardeen-Cooper-Schrieffer (BCS) state, exotic LO phase, and partially polarized free Fermi gas (NPP{N}_{\text{PP}}NPP​). The order of the phase transitions has been examined and, in particular, we find a weak first-order phase transition between the exotic inhomogeneous LO phase and the BCS phase. In comparison to the three-dimensional case, where the phase diagram is dominated by a generic separation phase, we predict a broader parameter space for the spatially inhomogeneous LO phase. By computing the superfluid density of the LO phase at different polarization, we show how the superfluidity of the system is suppressed with increasing spin polarization.
Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly 500 atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between spin imbalance, strong interactions, and superfluidity in an exotic phase of matter.
This thesis presents a theoretical study of Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) pairing states in inhomogeneous systems of cold atoms and of electrons. Features of spatially separated phases are explored, with particular focus on the behavior of the condensed phase and its experimental measures. Three specific systems are addressed below. First, we study bosonic atoms in three-dimensional optical lattices in the presence of an external spherical harmonic trapping potential. We investigate the critical value associated with the lattice depth and interaction strength below which the system undergoes a quantum phase transition from a global BEC phase to a coexistence of local BEC and Mott-insulating phases. We discuss the ground state properties, excitations, and experimental signatures of the condensate surrounded by the Mott-insulators. BCS pairing in fermionic atoms of two spin species that are confined to spatially separated trapping potentials is investigated next. We investigate the one-dimensional limit and find that, with increasing separation between the spin-dependent traps, the fermions undergo a transition from a global fully-paired phase to a coexistence of a fully-paired phase, a spin-imbalanced phase with oscillatory pairing, the so-called Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, and an unpaired completely spin-polarized phase. We present numerical profiles of key parameters of the phase diagram as well as observable signatures of the oscillatory pairing phase. The third topic is that of transport physics in a superconductor-ferromagnetic-metal (S/F) hybrid in which superconducting phases and ferromagnetic normal phases are artificially combined. We model the interface between the S and F regions and discuss possible scattering processes at the interface. We apply the Blonder-Tinkham-Klapwijk treatment with the interfacial model to calculate resistance of the system. These results explain recent experimental observations.
Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous superconducting and superfluid ground states, spontaneously breaking translation symmetries. In this Letter, we demonstrate that the transition from the FFLO to the normal state as a function of temperature or increased Fermi surface splitting is not a direct one. Instead, the system has an additional phase transition to a different state where pair-density-wave superconductivity (or superfluidity) exists only on the boundaries of the system, while the bulk of the system is normal. The surface pair-density-wave state is very robust and exists for much larger fields and temperatures than the FFLO state.