Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase

Abstract

We present an approximate gap equation for different crystalline structures of the LOFF phase of high density QCD at T=0. This equation is derived by using an effective condensate term obtained by averaging the inhomogeneous condensate over distances of the order of the crystal lattice size. The approximation is expected to work better far off any second order phase transition. As a function of the difference of the chemical potentials of the up and down quarks, $\delta \mu$, we get that the octahedron is energetically favored from $\delta \mu ={\Delta }_0/\sqrt{2}$ to $0.95{\Delta }_0$, where ${\Delta }_0$ is the gap for the homogeneous phase, while in the range $0.95{\Delta }_0-1.32{\Delta }_0$ the face centered cube prevails. At $\delta \mu =1.32{\Delta }_0$ a first order phase transition to the normal phase occurs.

11 pages, 5 figures

References in corpus (17)

• Inhomogeneous Superconductivity in Condensed Matter and QCD
• Color superconducting quark matter
• Crystalline Color Superconductivity
• The Crystallography of Color Superconductivity
• An effective field theory of QCD at high density
• Meson Masses in High Density QCD
• Aspects of high density effective theory in QCD
• Color Superconductivity in Compact Stars
• Effective Description of QCD at Very High Densities
• Dispersion Laws for In-medium Fermions and Gluons in the CFL Phase of QCD
• Hard Loops, Soft Loops, and High Density Effective Field Theory
• Novel Phases at High Density and their Roles in the Structure and Evolution of Neutron Stars
• Effective Field Theory for the Crystalline Colour Superconductive Phase of QCD
• Anisotropy Parameters for the Effective Description of Crystalline Color Superconductors
• Phonons and gluons in the crystalline color superconducting phase of QCD
• Quasi-particle Specific Heats for the Crystalline Color Superconducting Phase of QCD
• Crystalline Color Superconductivity: Effective Lagrangian and Phonon Dispersion Law

Cited by in corpus (26)

• Color superconductivity in dense quark matter
• Phases of Dense Quarks at Large N_c
• Interweaving Chiral Spirals
• Evaluating the Gapless Color-Flavor Locked Phase
• The Crystallography of Three-Flavor Quark Matter
• The rigidity of crystalline color superconducting quark matter
• A Hot Water Bottle for Aging Neutron Stars
• Crystalline chiral condensates off the tricritical point in a generalized Ginzburg-Landau approach
• LOFF Pairing vs. Breached Pairing in Asymmetric Fermion Superfluids
• Heating (Gapless) Color-Flavor Locked Quark Matter
• Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity
• Two-dimensional chiral crystals in the NJL model
• Chromomagnetic stability of the three flavor Larkin-Ovchinnikov-Fulde-Ferrell phase of QCD
• Self-consistent evaluation of quark masses in three flavor crystalline color superconductivity
• Stressed pairing in conventional color superconductors is unavoidable
• Dressed Polyakov loop and flavor dependent phase transitions
• Influence of finite quark chemical potentials on the three flavor LOFF phase of QCD
• On the ground state of gapless two flavor color superconductors
• Solid-state calculation of crystalline color superconductivity
• Dimensional Crossover in a Spin-imbalanced Fermi gas
• A diagrammatic derivation of the meson effective masses in the neutral color-flavor-locked phase of Quantum Chromodynamics
• LOFF and breached pairing with cold atoms
• Superfluid and Pseudo-Goldstone Modes in Three Flavor Crystalline Color Superconductivity
• Protocol to engineer Fulde-Ferrell-Larkin-Ovchinnikov states in a cold Fermi gas
• Ginzburg-Landau free energy of crystalline color superconductors: A matrix formalism from solid-state physics
• Topological Susceptibility in the Superconductive Phases of Quantum Chromodynamics: a Dyson-Schwinger Perspective