Inhomogeneous Superconductivity in Condensed Matter and QCD

Abstract

Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, differently from the usual BCS state, for the Cooper pair to have a non zero total momentum. For this reason in this state the gap varies in space, the ground state is inhomogeneous and a crystalline structure might be formed. This situation was considered for the first time by Fulde, Ferrell, Larkin and Ovchinnikov, and the corresponding state is called LOFF. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated to the presence of long wave-length excitations of zero mass. The situation described here is of interest both in solid state and in elementary particle physics, in particular in Quantum Chromo-Dynamics at high density and small temperature. In this review we present the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.

arXiv commentRevTex, 83 pages, 26 figures. Submitted to Review of Modern Physics

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• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• A real space auxiliary field approach to the BCS-BEC crossover
• Lattice structures of Larkin-Ovchinnikov-Fulde - Ferrell (LOFF) state
• Pairing dynamics and solitonic excitations in collisions of medium-mass, identical nuclei
• Bremsstrahlung neutrinos from electron-electron scattering in a relativistic degenerate electron plasma
• Superfluid density and Berezinskii-Kosterlitz-Thouless transition of a spin-orbit coupled Fulde-Ferrell superfluid
• Vortex lattice studies in CeCoIn5 with H perpendicular to c
• Quark matter contribution to the heat capacity of magnetized neutron stars
• Anomalous transition temperature oscillations in LOFF state
• Larkin-Ovchinnikov superfluidity in a two-dimensional imbalanced atomic Fermi gas
• Unconventional superconductivity with preformed pairs in twisted bilayer graphene
• Emergent anisotropy in the Fulde-Ferrell-Larkin-Ovchinnikov state
• Exploring emergent heterogeneous phases in strongly repulsive Fermi gases
• Extremely imbalanced two-dimensional electron-hole-photon systems
• Enhanced visibility of the Fulde-Ferrell-Larkin-Ovchinnikov state in one dimensional Bose-Fermi mixtures near the immiscibility point
• Phase Crystals
• Spin-Imbalanced Fermi Superfluidity in a Lieb Lattice Hubbard Model
• Topological Larkin-Ovchinnikov phase and Majorana zero mode chain in bilayer superconducting topological insulator films
• Anomalous specific heat jump in a two-component ultracold Fermi gas
• Influence of finite quark chemical potentials on the three flavor LOFF phase of QCD
• Pressure induced FFLO instability in multi-band superconductors
• Magnetic field-induced gapless state in multiband superconductors
• Rotating Fulde-Ferrell-Larkin-Ovchinnikov state in cold Fermi gases
• Magnetic structure of antiferromagnetic Fulde-Ferrell-Larkin-Ovchinnikov state
• Antiferromagnetic order in the FFLO state
• Attractive Hofstadter-Hubbard model with imbalanced chemical and vector potentials
• Fluctuation-Driven First-Order Transition in Pauli-limited d-wave Superconductors
• Dimensional Crossover of the Fulde-Ferrell-Larkin-Ovchinnikov State in Strongly Pauli-Limited Quasi-One-Dimensional Superconductors
• Collective modes of a soliton train in a Fermi superfluid
• Atom-dimer scattering length for fermions with different masses: analytical study of limiting cases
• Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
• Mechanism for enhancement of superconductivity in multi-band systems with odd parity hybridization
• Unconventional superconducting phases in a correlated two-dimensional Fermi gas of nonstandard quasiparticles: a simple model
• Out-of-Equilibrium Spin Transport in Mesoscopic Superconductors
• Solid-state calculation of crystalline color superconductivity
• Quasi-particle Specific Heats for the Crystalline Color Superconducting Phase of QCD
• Spatial noise correlations of a chain of ultracold fermions - A numerical study
• Chiral Modulations in Curved Space II: Conifold Geometries
• Quantum phases of a one-dimensional dipolar Fermi gas
• Dimensional Crossover in a Spin-imbalanced Fermi gas
• Antiferromagnetic superconductors with effective mass anisotropy in magnetic fields
• Disordered structures in ultracold spin-imbalanced Fermi gas
• Multiple phase separation in one-dimensional mixtures of mass- and population-imbalanced attractive Fermi gases
• Rashba versus Kohn-Luttinger: Evolution of p-wave superconductivity in magnetized two-dimensional Fermi gas subject to spin-orbit interaction
• Inhomogeneous superconductivity in the presence of time-reversal symmetry
• Inhomogeneity driven by Higgs instability in gapless superconductor
• Collective mode contributions to the Meissner effect: Fulde-Ferrell and pair-density wave superfluids
• Metric-space approach for distinguishing quantum phase transitions in spin-imbalanced systems
• Inhomogeneous state of few-fermion superfluids
• Stripe-ordered superfluid and supersolid phases in attractive Hofstadter-Hubbard model
• Unconventional fermionic pairing states in a monochromatically tilted optical lattice
• Synthetic nuclear Skyrme matter in imbalanced Fermi superfluids with a multicomponent order parameter
• Radial Fulde-Ferrell-Larkin-Ovchinnikov state in a population-imbalanced Fermi gas
• Helical ordering in the ground state of spin-one color superconductors as a consequence of parity violation
• Many-Body Phases of a Planar Bose-Einstein Condensate with Cavity-Induced Spin-Orbit Coupling
• Electromagnetic Proximity Effect: Superconducting Magnonics and Beyond
• Finite-Momentum Instability of Dynamical Axion Insulator
• Modulated phases of graphene quantum Hall polariton fluids
• NJL model of homogeneous neutral quark matter: Pseudoscalar diquark condensates revisited
• First- and Second-Order Phase Transitions, Fulde-Ferrel Inhomogeneous State and Quantum Criticality in Ferromagnet/Superconductor Double Tunnel Junctions
• Holographic superconductor induced by charge density waves
• Dimensional reduction in quantum field theories at finite temperature and density
• Transitions to the Fulde-Ferrell-Larkin-Ovchinnikov phases at low temperature in two dimensions
• Quantum condensation in electron-hole bilayers with density imbalance
• Aharonov-Bohm effect in superconducting LOFF state
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
• Mott Phase in Polarized Two-component Atomic Fermi Lattice Gas:A Playground for S=1/2 Heisenberg Model in Magnetic Field
• The Fulde-Ferrell-Larkin-Ovchinnikov State in the Organic Superconductor k-(BEDT-TTF)2Cu(NCS)2 as Observed in Magnetic Torque Experiments
• Pairing competition in a quasi-one-dimensional model of organic superconductors (TMTSF)${}_{2}X$ in magnetic field
• Feasibility of a Fulde-Ferrell-Larkin-Ovchinnikov superfluid Fermi atomic gas
• Unconventional superconductivity of an altermagnetic metal: Polarized BCS and inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states
• Topological Uniform Superfluid and FFLO Phases in 3D to 1D crossover of spin-orbit coupled Fermi gases
• Unusual Resistive Transitions in the Nodal-Line Semimetallic Superconductor NaAlSi
• Fulde-Ferrell-Larkin-Ovchinnikov state in bilayer dipolar systems
• Synthetic-gauge-field-induced resonances and Fulde-Ferrell-Larkin-Ovchinnikov states in a one-dimensional optical lattice
• Stability Analysis of Relativistic Polytropes
• Inhomogeneous superconducting states in two weakly linked superconducting ultra thin films
• Lattice QCD with mismatched Fermi surfaces
• Holographic entanglement entropy in imbalanced superconductors
• Effective potential and quantum criticality for imbalanced Fermi mixtures
• Ginzburg-Landau Analysis for the Antiferromagnetic Order in the Fulde-Ferrell-Larkin-Ovchinnikov Superconductor
• Josephson effect in an atomic Fulde-Ferrell-Larkin-Ovchinnikov superfluid
• Quantum size effect on the paramagnetic critical field in Pb nanofilms
• Proposed Fermi-surface reservoir-engineering and application to realizing unconventional Fermi superfluids in a driven-dissipative non-equilibrium Fermi gas
• Theory of generalized Josephson effects
• Fabry-Perot superconducting diode
• Correlated Phases of Population Imbalanced Fermi-Fermi Mixtures on an Optical Lattice
• Quantum normal-to-inhomogeneous superconductor phase transition in nearly two-dimensional metals
• LOFF and breached pairing with cold atoms
• Spectroscopic signatures of the Larkin-Ovchinnikov state in the conductance characteristics of a normal-metal/superconductor junction
• Collective modes in asymmetric ultracold Fermi systems
• Fulde-Ferrel-Larkin-Ovchinnikov Inhomogeneous Superconducting State and Phase Transitions Induced by Spin Accumulation in a Ferromagnet-$d_{x^2-y^2}$-Wave Superconductor-Ferromagnet Tunnel Junction
• Fermi-liquid theory of imbalanced quark matter
• Phase separations induced by a trapping potential in one-dimensional fermionic systems as a source of core-shell structures
• Spin-imbalanced ultracold Fermi gases in a two-dimensional array of tubes
• Intertwined Orders and the Physics of High Temperature Superconductors
• Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids
• Fulde-Ferrell-Larkin-Ovchinnikov superconductors near a surface
• Superfluid weight and Berezinskii-Kosterlitz-Thouless temperature of spin-imbalanced and spin-orbit-coupled Fulde-Ferrell phases in lattice systems
• Bound collective modes in nonuniform superconductors
• Orbital magnetism of ultracold fermionic gases in a lattice: dynamical mean-field approach
• Conductance spectroscopy of a correlated superconductor in a magnetic field in the Pauli limit: Evidence for strong correlations
• Pairing between Atoms and Molecules in a Boson-Fermion Resonant Mixture
• Inhomogeneous chiral symmetry breaking in noncommutative four fermion interactions
• Unconventional pairing in few-fermion systems at finite temperature
• Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor
• Anisotropic pressure in strange quark matter in the presence of a strong nonuniform magnetic field
• Protocol to engineer Fulde-Ferrell-Larkin-Ovchinnikov states in a cold Fermi gas
• p-wave Pairing in Two-Component Fermi System with Unequal Population: Weak Coupling BCS to Strong Coupling BEC Regimes
• Solitonic ground state in supersymmetric theory in background
• P-wave Pairing in Two-Component Fermi Systems with Unequal Population near Feshbach Resonance
• Triplet pair correlations in {\it s-}wave superfluids as a signature of the FFLO state
• Minimal Model for an Unbalanced Holographic Superconductor
• 1D-FFLO state in the absence of time-reversal symmetry breaking
• Generic nodeless Larkin Ovchinnikov states due to singlet-triplet mixing
• Superfluidity in density imbalanced bilayers of dipolar fermions
• Nonequilibrium BCS-BEC crossover and unconventional FFLO superfluid in a strongly interacting driven-dissipative Fermi gas
• Multi-orbital Fulde-Ferrell-Larkin-Ovchinnikov State in SrTiO_3 Heterostructures
• Triplet-odd pairing in finite nuclear systems: Even-even singly closed nuclei
• Some aspects of color superconductivity: an introduction
• Quantum Pairing Time Orders
• Quantum Lifshitz points in an altermagnetic metal
• Unconventional superconductivity in iron-base superconductors in a three-band model
• Andreev reflection between a normal metal and the FFLO superconductor II: a self-consistent approach
• Dynamical instability towards finite-momentum pairing in quenched BCS superconducting phases
• Analytic Baby Skyrmions at Finite Density
• Renormalization group approach to spinor Bose-Fermi mixtures in a shallow optical lattice
• Gapless Higgs Mode in the Fulde-Ferrell-Larkin-Ovchinnikov State of a Superconductor
• Relativistic anisotropic stars with the polytropic equation of state in general relativity
• Majorana modes in striped two-dimensional inhomogeneous topological superconductors
• Fulde-Ferrell-Larkin-Ovchinnikov State in Perpendicular Magnetic Fields in Strongly Pauli-Limited Quasi-Two-Dimensional Superconductors
• Antiferromagnetic Phases in the Fulde-Ferrell-Larkin-Ovchinnikov State of CeCoIn_5
• Is gluonic color-spin locked phase stable?
• Singular Vortex in Narrow Cylinders of Superfluid 3He-A Phase
• Fulde-Ferrell superfluids in spinless ultracold Fermi gases
• Multi-particle instability in a spin-imbalanced Fermi gas
• Larkin-Ovchinikov superfluidity in time-reversal symmetric bilayer Fermi gases
• Non-commutative dynamics and roton-like spectra in bosonic and fermionic condensates
• Lifshitz transitions induced by magnetic field
• Stabilising Fulde-Ferrel-Larkin-Ovchinnikov Superfluidity with long-range Interactions in a mixed dimensional Bose-Fermi System
• Stabilization of the Fulde-Ferrell-Larkin-Ovchinnikov State by Tuning In-plane Magnetic-Field Direction: Application to a Quasi-One-Dimensional Organic Superconductor
• Quantum criticality in inter-band superconductors
• Diffusion Monte Carlo study of a spin-imbalanced two-dimensional Fermi gas with attractive interactions
• On the robustness of solitons crystals in the Skyrme model
• Lifshitz tricritical point and its relation to the FFLO superconducting state
• Antiferromagnetic fluctuations and the Fulde-Ferrell-Larkin-Ovchinnikov state in CeCoIn5
• Color superconductivity in ultra-dense quark matter
• Two-dimensional spin-imbalanced Fermi gases at non-zero temperature: Phase separation of a non-condensate
• Meissner screening masses in gluonic phase
• Andreev-Bragg reflection from an Amperian superconductor
• Creation of a degenerate Bose-Bose mixture of erbium and lithium atoms
• Color superconductivity and the strange quark
• Connection between in-plane upper critical field $H_{c2}$ and gap symmetry in layered $d$-wave superconductors revisited
• Anomalous magnetic transition in a disordered quasicrystal approximant with heavy-fermion nature
• Exact mapping from the $(3+1)$-dimensional Skyrme model to the $(1+1)$-dimensional sine-Gordon theory and some applications
• Enhanced Fulde-Ferrell-Larkin-Ovchinnikov and Sarma superfluid states near an orbital Feshbach resonance
• Superfluid density reduction and spin-imbalanced pairing in a fermionic superfluid due to dynamical boson exchange
• Pairing in spin polarized two-species fermionic mixtures with mass asymmetry
• The phase diagram of two-dimensional fast-rotating ultra-cold fermionic atoms near unitarity
• Pairing in population imbalanced Fermion systems
• Finite momentum condensation in a pumped microcavity
• Ginzburg-Landau free energy of crystalline color superconductors: A matrix formalism from solid-state physics
• Topological Fulde-Ferrell Superfluids in Triangular Lattices
• The Gor'kov and Melik-Barkhudarov correction to the mean-field critical field transition to Fulde-Ferrell-Larkin-Ovchinnikov states
• Repulsive Fermi and Bose Polarons in Quantum Gases
• Collective modes in Fulde-Ferrell-Larkin-Ovchinnikov superconductors: The role of long-range Coulomb interaction and signatures in density response
• Detecting Topological Phase Transition in Superconductor-Semiconductor Hybrids by Electronic Raman Spectroscopy
• In-plane magnetic field-induced orbital FFLO superconductivity in twisted WSe${}_2$ homobilayers
• Altermagnetism-driven FFLO superconductivity in finite-filling 2D lattices
• The Gor'kov and Melik-Barkhudarov correction to an imbalanced Fermi gas in the presence of impurities
• Fulde-Ferrell states in unequally charged Fermi gases
• Magnetic properties of the Larkin-Ovchinnikov-Fulde-Ferrell superconducting phase
• Phase diagram of two-flavor quark matter: Gluonic phase at nonzero temperature
• Oscillations of magnetization and conductivity in anisotropic Fulde-Ferrell-Larkin-Ovchinnikov superconductors
• Fluctuations in a superconducting quantum critical point of multi-band metals
• Exploring Exotic Superfluidity of Polarized Ultracold Fermions in Optical Lattices
• From Trapped Atoms to Liberated Quarks
• Competing order parameters and a tricritical point with a difference
• Quark Confinement and the Fractional Quantum Hall Effect
• Multiple polaron quasiparticles with dipolar fermions in a bilayer geometry
• The three flavor LOFF phase of QCD
• Phase diagram for the trapped p-wave fermionic superfluid with population imbalance
• Superconductivity with deformed Fermi surfaces and compact stars
• BCS-BEC Crossover in Two-Dimensional Attractive Hubbard Model under Magnetic Field
• Hierarchy of pairing in imbalanced three-component one-dimensional Fermi gas
• Quantitative Probe of Pairing Correlations in a Cold Fermionic Atom Gas
• Interplay of mass imbalance and frustration in correlated band insulators
• A domain wall and chiral edge currents in holographic chiral phase transitions
• Introduction to High-Temperature Superconductivity for Solid State Chemists
• Some recent progress on quark pairings in dense quark and nuclear matter
• Pair-mixing induced Time-reversal-breaking superconductivity
• Color superconductivity in high density QCD
• Stability Analysis Of Fractional Relativistic Polytropes
• Fulde-Ferrell superfluids in an asymmetric three-component Fermi Gas
• Theoretical study of interacting electrons in one dimension - ground states and experimental signatures
• Color-superconductivity and inhomogeneous chiral symmetry breaking in isospin-asymmetric quark matter
• Exploring Strongly Interacting Gapless States: Cuprates, Pair Density Waves, and Fluctuating Superconductivity
• BCS-BEC crossover in a quasi-two-dimensional Fermi superfluid
• Exploring new states of matter with a photonic emulator
• Breached pair superfluidity: a brief review
• Topological Fulde-Ferrell and Larkin-Ovchinnikov states in spin-orbit coupled lattice system
• Unconventional pairing in few-fermion systems tuned by external confinement
• Finite momentum condensate brought on by Zeeman field
• Field-induced topological pair-density wave states in a multilayer optical lattice
• Supersymmetric construction of self-consistent condensates in large N GN model: solitons on finite-gap potentials
• Axial anomaly and nesting in the inhomogeneous chiral phase
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Phase transitions in the inner crust of neutron stars within the superfluid band theory: Competition between ${}^1{\text{S}}_0$ pairing and spin polarization under finite temperature and magnetic field