Crystalline Color Superconductivity

Abstract

In any context in which color superconductivity arises in nature, it is likely to involve pairing between species of quarks with differing chemical potentials. For suitable values of the differences between chemical potentials, Cooper pairs with nonzero total momentum are favored, as was first realized by Larkin, Ovchinnikov, Fulde and Ferrell (LOFF). Condensates of this sort spontaneously break translational and rotational invariance, leading to gaps which vary periodically in a crystalline pattern. Unlike the original LOFF state, these crystalline quark matter condensates include both spin zero and spin one Cooper pairs. We explore the range of parameters for which crystalline color superconductivity arises in the QCD phase diagram. If in some shell within the quark matter core of a neutron star (or within a strange quark star) the quark number densities are such that crystalline color superconductivity arises, rotational vortices may be pinned in this shell, making it a locus for glitch phenomena.

40 pages, LaTeX with eps figs. v2: New paragraph on Ginzburg-Landau treatment of LOFF phase in section 5. References added. v3: Small changes only. Version to appear in Phys. Rev. D

References in corpus (14)

• QCD at finite isospin density
• Color superconductivity in weak coupling
• Probing strange stars and color superconductivity by r-mode instabilities in millisecond pulsars
• Magnetic fields within color superconducting neutron star cores
• Quark Hadron Continuity in QCD with one Flavor
• Prospects of Detecting Baryon and Quark Superfluidity from Cooling Neutron Stars
• Dense QCD : Overhauser or BCS Pairing ?
• A chiral crystal in cold QCD matter at intermediate densities?
• The Transition Temperature to the Superconducting Phase of QCD at High Baryon Density
• On the QCD Ground State at High Density
• Neutrino Propagation In Color Superconducting Quark Matter
• Non-Fermi Liquid Behaviour, the BRST Identity in the Dense Quark-Gluon Plasma and Color Superconductivity
• On the Applicability of Weak-Coupling Results in High Density QCD
• How to Renormalize the Gap Equation in High Density QCD

Cited by in corpus (304)

• Color superconductivity in dense quark matter
• NJL-model analysis of dense quark matter
• The phase diagram of dense QCD
• Strange Quark Matter and Compact Stars
• Phases of Dense Quarks at Large N_c
• Hybrid stars that masquerade as neutron stars
• Physics of Neutron Star Crusts
• Inhomogeneous Superconductivity in Condensed Matter and QCD
• QCD and strongly coupled gauge theories: challenges and perspectives
• The Physics of Pair Density Waves
• Interior Gap Superfluidity
• The Minimal CFL-Nuclear Interface
• Asymmetric Two-component Fermion Systems in Strong Coupling
• Inhomogeneous chiral condensates
• Quark matter in compact stars?
• The phase diagram of neutral quark matter: Self-consistent treatment of quark masses
• Electric fields at the quark surface of strange stars in the color-flavor locked phase
• Gapless two-flavor color superconductor
• Maximum elastic deformations of compact stars with exotic equations of state
• High Density Quark Matter under Stress
• Gravity Dual of Spatially Modulated Phase
• Compact stars with color superconducting quark matter
• Absence of two-flavor color-superconductivity in compact stars
• The Crystallography of Color Superconductivity
• BEC-BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids
• Gapless Color-Flavor-Locked Quark Matter
• Solid Quark Stars?
• QCD-like Theories at Finite Baryon and Isospin Density
• Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
• Two lectures on color superconductivity
• Advances in perturbative thermal field theory
• Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics
• Implications of the measurement of pulsars with two solar masses for quark matter in compact stars and HIC. A NJL model case study
• How many phases meet at the chiral critical point?
• Flavor-Mixing Effects on the QCD Phase Diagram at non-vanishing Isospin Chemical Potential: One or Two Phase Transitions?
• Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases
• Isospin Chemical Potential and the QCD Phase Diagram at Nonzero Temperature and Baryon Chemical Potential
• Gapless color superconductivity at zero and at finite temperature
• Quasi-one-dimensional polarized Fermi superfluids
• Topological Fulde-Ferrel-Larkin-Ovchinnikov states in Spin-orbit Coupled Fermi Gases
• A calculation of the QCD phase diagram at finite temperature, and baryon and isospin chemical potentials
• Role of Vector Interaction and Axial Anomaly in the PNJL Modeling of the QCD Phase Diagram
• Breached pairing superfluidity: Possible realization in QCD
• Fluctuations and phase transitions in Larkin-Ovchinnikov liquid crystal states of population-imbalanced resonant Fermi gas
• Equation of state for the MCFL phase and its implications for compact star models
• Semi-superfluid strings in High Density QCD
• Charge Neutrality Effects on 2-flavor Color Superconductivity
• Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications
• Density-Matrix Renormalization Group Study of Trapped Imbalanced Fermi Condensates
• Chromomagnetic Instability and the LOFF state in a two flavor Color Superconductor
• Screening masses in neutral two-flavor color superconductor
• Interweaving Chiral Spirals
• Evaluating the Gapless Color-Flavor Locked Phase
• Fluctuations in the quark-meson model for QCD with isospin chemical potential
• Extensive study of phase diagram for charge neutral homogeneous quark matter affected by dynamical chiral condensation -- unified picture for thermal unpairing transitions from weak to strong coupling --
• Mixed phases of color superconducting quark matter
• The Crystallography of Three-Flavor Quark Matter
• Effective Lagrangian and Topological Interactions in Supersolids
• Pairing in a two-component ultracold Fermi gas: phases with broken space symmetries
• Single color and single flavor color superconductivity
• Superfluid phases of quark matter. III. Supercurrents and vortices
• The ground state in a spin-one color superconductor
• The Stability of Strange Star Crusts and Strangelets
• Magnetic Phases in Three-Flavor Color Superconductivity
• Instanton Effects in QCD at High Baryon Density
• Analytical and numerical evaluation of the Debye and Meissner masses in dense neutral three-flavor quark matter
• A Hot Water Bottle for Aging Neutron Stars
• The NJL model of dense three-flavor matter with axial anomaly: the low temperature critical point and BEC-BCS diquark crossover
• The rigidity of crystalline color superconducting quark matter
• Thermodynamics of chiral symmetry at low densities
• Reaction rates and transport in neutron stars
• Phase diagram of dense neutral three-flavor quark matter
• Ginzburg-Landau approach to the three flavor LOFF phase of QCD
• Gluonic phase in neutral two-flavor dense QCD
• Equilibrium sequences of non rotating and rapidly rotating crystalline color superconducting hybrid stars
• Signatures for quark matter from multi-messenger observations
• Crystalline chiral condensates off the tricritical point in a generalized Ginzburg-Landau approach
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• LOFF Pairing vs. Breached Pairing in Asymmetric Fermion Superfluids
• Pion Condensation in Baryonic Matter: from Sarma Phase to Larkin-Ovchinnikov-Fudde-Ferrell Phase
• Effective Description of QCD at Very High Densities
• Electromagnetic Meissner effect in spin-one color superconductors
• Anisotropic admixture in color-superconducting quark matter
• Meson Supercurrent State in High Density QCD
• Heating (Gapless) Color-Flavor Locked Quark Matter
• Phase Structure of 2-Flavor Quark Matter: Heterogeneous Superconductors
• Structure of the electrospheres of bare strange stars
• Mass Terms in Effective Theories of High Density Quark Matter
• A note on color neutrality in NJL-type models
• Unified weak/strong coupling framework for nuclear matter and neutron stars
• Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity
• Solitonic ground states in (color-) superconductivity
• Quakes in Solid Quark Stars
• A Diagrammatic Approach to Crystalline Color Superconductivity
• Pion and kaon condensation in a 3-flavor NJL model
• Novel Lifshitz point for chiral transition in the magnetic field
• Phase diagram of two-color quark matter at nonzero baryon and isospin density
• Neutrino emission and cooling rates of spin-one color superconductors
• The Meissner Effect in a Two Flavor LOFF Color Superconductor
• Ladder-QCD at finite isospin chemical potential
• Neutrino Emission from Ungapped Quark Matter
• Fireballs from Quark Stars in the CFL Phase: Application to Gamma Ray Bursters
• Direct Urca neutrino rate in colour superconducting quark matter
• Colour superconductivity in finite systems
• Color superconductivity vs. pseudoscalar condensation in a three-flavor NJL model
• Rapid cooling of the compact star in Cassiopea A as a phase transition in dense QCD
• Effect of entrainment on stress and pulsar glitches in neutron star crust
• Spontaneous current generation in the gapless 2SC phase
• The effect of population imbalance on the Berezinskii-Kosterlitz-Thouless phase transition in a superfluid Fermi gas
• Unbalanced Holographic Superconductors and Spintronics
• Mass-Induced Crystalline Color Superconductivity
• Neutrino emission from compact stars and inhomogeneous color superconductivity
• Is PSR B0943+10 a low-mass quark star?
• Quantum phase diagram of fermion mixtures with population imbalance in one-dimensional optical lattices
• Bulk viscosity in 2SC quark matter
• A Neutral Two Flavor Loff Color Superconductor
• Neutral Larkin--Ovchinnikov--Fulde--Ferrell state and chromomagnetic instability in two-flavor dense QCD
• Opening the Crystalline Color Superconductivity Window
• Bulk viscosity in kaon-condensed color-flavor locked quark matter
• Neutrino scattering off pair-breaking and collective excitations in superfluid neutron matter and in color-flavor locked quark matter
• Chromomagnetic Instability and Induced Magnetic Field in Neutral Two-Flavor Color Superconductivity
• Two-dimensional chiral crystals in the NJL model
• Stability conditions and Fermi surface topologies in a superconductor
• Quark stars under strong magnetic fields
• Characterizing the Larkin-Ovchinnikov-Fulde-Ferrel phase induced by the chromomagnetic instability
• Properties of Bare Strange Stars Associated with Surface Electric Fields
• Constraining crystalline color superconducting quark matter with gravitational-wave data
• How do chiral condensates affect color superconducting quark matter under charge neutrality constraints?
• Gravitational radiation from crystalline color-superconducting hybrid stars
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Meson supercurrents and the Meissner effect in the Sakai-Sugimoto model
• Enhancement effect of mass imbalance on Fulde-Ferrell-Larkin-Ovchinnikov type of pairing in Fermi-Fermi mixtures of ultracold quantum gases
• The phase diagram of neutral quark matter: The effect of neutrino trapping
• Chromomagnetic stability of the three flavor Larkin-Ovchinnikov-Fulde-Ferrell phase of QCD
• Spontaneous Superfluid Current Generation in CFL at Nonzero Strange Quark Mass
• Phases of asymmetric nuclear matter with broken space symmetries
• Tidal deformations of compact stars with crystalline quark matter
• Quark core impact on hybrid star cooling
• Imbalanced Fermi superfluid in a one-dimensional optical potential
• Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density
• Magnetized color flavor locked state and compact stars
• Gravitational Waves From Low Mass Neutron Stars
• A low energy theory for superfluid and solid matter and its application to the neutron star crust
• Dualities and inhomogeneous phases in dense quark matter with chiral and isospin imbalances in framework of effective model
• Equations of state and stability of color-superconducting quark matter cores in hybrid stars
• Supersymmetric Color Superconductivity
• On the possible sources of gravitational wave bursts detectable today
• Novel Topological Effects in Dense QCD in a Magnetic Field
• Phase diagram of chiral quark matter: Fulde-Ferrell pairing from weak to strong coupling
• Meson current in the CFL phase
• Probing hybrid stars with gravitational waves via interfacial modes
• Self-consistent evaluation of quark masses in three flavor crystalline color superconductivity
• Anisotropy Parameters for the Effective Description of Crystalline Color Superconductors
• Transport theory for cold relativistic superfluids from an analogue model of gravity
• Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase
• Neutrality of a magnetized two-flavor quark superconductor
• Stressed pairing in conventional color superconductors is unavoidable
• Meissner Effect and Vortex Dynamics in Quark Stars -- A Model for Soft Gamma-Ray Repeaters
• Gluonic phase versus LOFF phase in two-flavor quark matter
• Quark matter in neutron stars
• Quantum liquid-crystal order in resonant atomic gases
• Critical temperature for kaon condensation in color-flavor locked quark matter
• Two-layer compact stars with crystalline quark matter: Screening effect on the tidal deformability
• Instability of Fulde-Ferrell-Larkin-Ovchinnikov states in three and two dimensions
• Miscibility in a degenerate fermionic mixture induced by linear coupling
• Evidence for BCS Diquark Condensation in the 3+1d Lattice NJL Model
• Larkin-Ovchinnikov-Fulde-Ferrell state in two-color quark matter
• Self-bound models of compact stars and recent mass-radius measurements
• Phonons and gluons in the crystalline color superconducting phase of QCD
• Crystalline ground state in chiral Gross-Neveu and Cooper pair models at finite densities
• Ring solitons and soliton sacks in imbalanced fermionic systems
• Breaking rotational symmetry in two-flavor color superconductors
• Phase separation in imbalanced fermion superfluids beyond mean-field
• Dense quark matter in compact stars
• Thickness of the strangelet-crystal crust of a strange star
• Analytic SU(N) Skyrmions at finite Baryon density
• Collective excitations, instabilities, and ground state in dense quark matter
• Superfluid states with moving condensate in nuclear matter
• Finite temperature phase diagram of trapped Fermi gases with population imbalance
• Phases of Gauge Theories
• Electromagnetic signals from bare strange stars
• Pair-density-wave superconductivity of faces, edges and vertices in systems with imbalanced fermions
• Worldline Monte Carlo for fermion models at large N_f
• Manifestation of Instabilities in Nambu-Jona-Lasinio type models
• Angular Momentum Mixing in Crystalline Color Superconductivity
• Numerical Portrait of a Relativistic BCS Gapped Superfluid
• Ginzburg-Landau phase diagram for dense matter with axial anomaly, strange quark mass, and meson condensation
• Stable configurations of hybrid stars with colour-flavour-locked core
• Crystalline phases by an improved gradient expansion technique
• Polarized Fermi gases at finite temperature in the BCS-BEC crossover
• Self-consistent parametrization of the two-flavor isotropic color-superconducting ground state
• Nonuniform phases in a three-flavor Nambu--Jona-Lasinio model
• Thermal evolution of massive compact objects with dense quark cores
• Goldstone boson currents in a kaon condensed CFL phase
• Phase transitions and resilience of the MDCDW phase at finite temperature and density
• Gluonic phases, vector condensates, and exotic hadrons in dense QCD
• Surface pair-density-wave superconducting and superfluid states
• Quark beta decay in the inhomogeneous chiral phase and cooling of compact stars
• QCD at high density/temperature
• Cooling compact stars and phase transitions in dense QCD
• Gapless phases of color-superconducting matter
• Phase diagram of the non-uniform chiral condensate in different regularization schemes at T=0
• Analytic multi-Baryonic solutions in the SU(N)-Skyrme model at finite density
• Mystery of Excess Low Energy States in a Disordered Superconductor in a Zeeman Field
• Quench dynamics of spin-imbalanced Fermi-Hubbard model in one dimension
• Diquark condensation at strong coupling
• Brane nucleation instabilities in non-AdS/non-CFT
• Structure of Compact Stars in Pion Superfluid Phase
• Color superfluidity of neutral ultra-cold fermions in the presence of color-flip and color-orbit fields
• Single-flavour and two-flavour pairing in three-flavour quark matter
• Diquark Bose-Einstein condensation
• The Crystallography of Strange Quark Matter
• Lattice gauge theory with baryons at strong coupling
• Quark matter contribution to the heat capacity of magnetized neutron stars
• Chromomagnetic instability in two-flavor quark matter at nonzero temperature
• Influence of finite quark chemical potentials on the three flavor LOFF phase of QCD
• Effect of temperature and magnetic field on two-flavor superconducting quark matter
• Torsional oscillations of crystalline color-superconducting hybrid stars: Possible sources for Advanced LIGO?
• Spontaneous symmetry breaking in strong-coupling lattice QCD at high density
• Torsional oscillations of nonbare strange stars
• Anomalous specific heat jump in a two-component ultracold Fermi gas
• Antichiral and nematicity-wave superconductivity
• On the ground state of gapless two flavor color superconductors
• Quasi-particle Specific Heats for the Crystalline Color Superconducting Phase of QCD
• Dimensional Crossover in a Spin-imbalanced Fermi gas
• Classical and relativistic dynamics of supersolids: variational principle
• Meissner screening mass in two-flavor quark matter at nonzero temperature
• Chiral density wave versus pion condensation in the 1+1 dimensional NJL model
• Solid-state calculation of crystalline color superconductivity
• NJL model of homogeneous neutral quark matter: Pseudoscalar diquark condensates revisited
• Inhomogeneity driven by Higgs instability in gapless superconductor
• Radial Fulde-Ferrell-Larkin-Ovchinnikov state in a population-imbalanced Fermi gas
• Consistent regularization and renormalization in models with inhomogeneous phases
• Phase diagram of chiral quark matter: color and electrically neutral Fulde-Ferrell phase
• Cosmic ray strangelets
• A diagrammatic derivation of the meson effective masses in the neutral color-flavor-locked phase of Quantum Chromodynamics
• Helical ordering in the ground state of spin-one color superconductors as a consequence of parity violation
• Illuminating Dense Quark Matter
• The shear viscosity of two-flavor crystalline color superconducting quark matter
• Dynamics near QCD critical point by dynamic renormalization group
• Crystalline Color Superconductivity: Effective Lagrangian and Phonon Dispersion Law
• Proposal for interferometric detection of topological defects in modulated superfluids
• Topological Uniform Superfluid and FFLO Phases in 3D to 1D crossover of spin-orbit coupled Fermi gases
• Reply to Comment on Strangelets as Cosmic Rays beyond the Greisen-Zatsepin-Kuzmin Cutoff
• Feasibility of a Fulde-Ferrell-Larkin-Ovchinnikov superfluid Fermi atomic gas
• Lattice QCD with mismatched Fermi surfaces
• LOFF and breached pairing with cold atoms
• Quark Matter in Neutron Stars: An apercu
• BCS-BEC Crossover and Stability in a Nambu-Jona-Lasinio Model with Diquark-Diquark Repulsion
• Massive quark effects in two flavor color superconductors
• Fractons in effective field theories for spontaneously broken translations
• Alpha-cluster structure and density wave in oblate nuclei
• Holographic Magnetized Chiral Density Wave
• Intertwined Orders and the Physics of High Temperature Superconductors
• Anomaly and a QCD-like phase diagram with massive bosonic baryons
• Inhomogeneous chiral symmetry breaking in noncommutative four fermion interactions
• Strangeness in Neutron Stars
• Superfluid and Pseudo-Goldstone Modes in Three Flavor Crystalline Color Superconductivity
• Neutrino Emission From Direct Urca Processes in Pion Condensed Quark Matter
• Exploring phases of dense QCD with compact stars
• General Quasiparticle Propagator and Mass Dependence in Degenerate Color Superconductivity
• Protocol to engineer Fulde-Ferrell-Larkin-Ovchinnikov states in a cold Fermi gas
• Non-leptonic weak processes in spin-one color superconducting quark matter
• Resummed one-loop gluonic contributions to the color superconducting color charge density vanish
• Isospin and density dependences of nuclear matter symmetry energy coefficients II
• Superfluidity in density imbalanced bilayers of dipolar fermions
• Pairing in Asymmetrical Fermi Systems with Intra- and Inter-Species Correlations
• Analytic Baby Skyrmions at Finite Density
• Color superconductivity in the Nambu Jona-Lasinio model complemented by a Polyakov loop
• Thermal phonon fluctuations and stability of the magnetic dual chiral density wave phase in dense QCD
• Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu--Jona-Lasinio model
• New modeling for hybrid stars with an elastic quark core
• Two tricritical lines from a Ginzburg-Landau expansion: application to the LOFF phase
• Translational Symmetry Breaking in Higgs & Gauge Theory, and the Cosmological Constant
• Is gluonic color-spin locked phase stable?
• Trapping Dirac fermions in tubes generated by two scalar fields
• Lifshitz tricritical point and its relation to the FFLO superconducting state
• Astrophysical aspects of neutrino dynamics in ultra-degenerate quark gluon plasma
• Pulsar as a Weber detector of gravitational waves and a probe to its internal phase transitions
• Exact mapping from the $(3+1)$-dimensional Skyrme model to the $(1+1)$-dimensional sine-Gordon theory and some applications
• Ground state fractal crystals
• Differential rotation in neutron stars with open and closed magnetic topologies
• Generalized Nambu-Goldstone pion in dense matter: a schematic NJL model
• Meissner screening masses in gluonic phase
• BCS vs Overhauser pairing in dense (2+1)d QCD
• How Neutron Star Observations Point Towards Exotic Matter: Existing Explanations and a Prospective Proposal
• Ginzburg-Landau free energy of crystalline color superconductors: A matrix formalism from solid-state physics
• Inhomogeneous chiral phase in the magnetic field
• Phase diagram of two-flavor quark matter: Gluonic phase at nonzero temperature
• Trapping of Spin-0 fields on tube-like topological defects
• Berry Curvature and Spin-One Color Superconductivity
• Higher Angular Momentum Mixing in a Non-spherical Color Superconductor with Time Reversal Invariance Violation
• Phases of Hadron-Quark Matter in (Proto) Neutron Stars
• Thermodynamic and hydrodynamic characteristics of interacting system formed in relativistic heavy ion collisions
• Hierarchy of pairing in imbalanced three-component one-dimensional Fermi gas
• Competing order parameters and a tricritical point with a difference
• Some recent progress on quark pairings in dense quark and nuclear matter
• Pairing fluctuation effects in a strongly coupled color superfluid/superconductor
• Overview of Crystalline Color Superconductors
• Mass Effect in Single Flavor Color Superconductivity
• Dense baryonic matter in strong coupling lattice gauge theory
• Finite momentum condensate brought on by Zeeman field
• Effective Fields in Dense Quantum Chromodynamics
• Meson Exchange Effect on Color Superconductivity