Supercurrents in color-superconducting quark matter

We review the basic properties of the currCFL-K⁰ phase in dense quark matter. At asymptotically large densities, three-flavor quark matter is in the color-flavor locked (CFL) state. The currCFL-K⁰ state is a way to respond to “stress” on the quark Cooper pairing, imposed at more moderate densities by the strange quark mass and the conditions of electric and color neutrality. We show how a kaon supercurrent is incorporated in a purely fermionic formalism, and show that the net current vanishes due to cancellation of fermion and charge-conjugate fermion contributions.     

Nonlocality effects on spin-one pairing patterns in two-flavor color superconducting quark matter and compact star applications

We study the influence of nonlocality in the interaction on two spin-one pairing patterns of two-flavor quark matter: the anisotropic blue-color pairing besides the usual two-color superconducting matter (2SCb), in which red and green colors are paired, and the color-spin locking phase (CSL). The effect of nonlocality on the gaps is rather large and the pairings exhibit a strong dependence on the form factor of the interaction, especially in the low-density region. The application of these small spin-one condensates for compact stars is analyzed: the early onset of quark matter in the nonlocal models may help to stabilize hybrid star configurations. While the anisotropic blue-quark pairing does not survive a big asymmetry in flavor space as imposed by the charge neutrality condition, the CSL phase as a flavor independent pairing can be realized as neutral matter in compact star cores. However, smooth form factors and the mismatch between the flavor chemical potential in neutral matter make the effective gaps of the order of magnitude ≃10 keV, and a more systematic analysis is needed to decide whether such small gaps could be consistent with the cooling phenomenology. The text was submitted by the authors in English.     

Neutral Larkin-Ovchinnikov-Fulde-Ferrell state and chromomagnetic instability in two-flavor dense QCD

In two-flavor dense quark matter, we describe the dynamics in the single plane wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state satisfying the color and electric neutrality conditions. We find that because the neutral LOFF state itself suffers from a chromomagnetic instability in the whole region where it coexists with the (gapped or gapless) two-flavor superconducting phases, it cannot cure this instability in those phases. This is unlike the recently revealed gluonic phase which seems to be able to resolve this problem.     

Electrical Neutrality and Symmetry Restoring Phase Transitions at High Density in a Two-Flavor Nambu-Jona-Lasinio Model

A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value of m0/∧ from QCD phenomenology, the phase transition must be of the first order.     

Neutral color-spin-locking phase in neutron stars

We present results for the spin-1 color-spin-locking (CSL) phase using a NJL-type model in two-flavor quark matter for compact stars applications. The CSL condensate is flavor symmetric and therefore charge and color neutrality can easily be satisfied. We find small energy gaps ≃ 1MeV, which make the CSL matter composition and the EoS not very different from the normal quark matter phase. We keep finite quark masses in our calculations and obtain no gapless modes that could have strong consequences in the late cooling of neutron stars. Finally, we show that the region of the phase diagram relevant for neutron star cores, when asymmetric flavor pairing is suppressed, could be covered by the CSL phase.     

Color superconducting matter in a magnetic field

We investigate the effect of a magnetic field on cold dense quark matter using an effective model with four-Fermi interactions. We find that the gap parameters representing the predominant pairing between the different quark flavors show oscillatory behavior as a function of the magnetic field. We point out that due to electric and color neutrality constraints the magnetic fields as strong as presumably existing inside magnetars might induce significant deviations from the gap structure at a zero magnetic field.     

Breached pairing superfluidity: possible realization in QCD

We propose a wide universality class of gapless superfluids, and analyze a limit that might be realized in quark matter at intermediate densities. In the breached pairing color superconducting phase heavy s quarks, with a small Fermi surface, pair with light u or d quarks. The ground state has a superfluid and a normal Fermi component simultaneously. We expect a second-order phase transition, as a function of increasing density, from the breached pairing phase to the conventional color-flavor locked phase.     

Study of Strange Quark Mass in CFL Phase

In this paper we introduce bilocal fields in the global color symmetry model and consider color and electrical neutrality conditions simultaneously to study the effect of strange quark mass Ms for the momentum-dependent condensate of color-flavor locked phase. Consequently we find that there will be a quantum phase transition occurring.     

Phase transition to color-flavor-locked matter and condensation of Goldstone bosons in neutron star matter

Deconfinement phase transition and condensation of Goldstone bosons in neutron star matter are investigated in a chiral hadronic model (also referred as to the FST model) for the hadronic phase (HP) and in the color-flavor-locked (CFL) quark model for the deconfined quark phase. It is shown that the hadronic-CFL mixed phase (MP) exists in the center of neutron stars with a small bag constant, while the CFL quark matter cannot appear in neutron stars when a large bag constant is taken. Color superconductivity softens the equation of state (EOS) and decreases the maximum mass of neutron stars compared with the unpaired quark matter. The K⁰ condensation in the CFL phase has no remarkable contribution to the EOS and properties of neutron star matter. The EOS and the properties of neutron star matter are sensitive to the bag constant B, the strange quark mass m_s and the color superconducting gap Δ. Increasing B and m_s or decreasing Δ can stiffen the EOS which results in the larger maximum masses of neutron stars.     

Full phase diagram of the massive Gross-Neveu model

The massive Gross-Neveu model is solved in the large-N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi elliptic functions. It contains three parameters which are determined by transcendental equations. Self-consistency of the scalar potential is proved. The phase diagram for non-zero bare quark mass is found to contain a kink-antikink crystal phase as well as a massive fermion gas phase featuring a cross-over from light to heavy effective fermion mass. For zero bare quark mass, we recover the three known phases kink-antikink crystal, massless fermion gas, and massive fermion gas. All phase transitions are shown to be of second order. Equations for the phase boundaries are given and solved numerically. Implications on condensed matter physics are indicated where our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.     

Color Superconductivity in Cold Dense Quark Matter

We investigate the phase structure of color superconducting quark matter at intermediate densities for two- and three-flavor systems. We thereby focus our attention on the influence of charge neutrality conditions as well as -equilibrium of the different phases. These constraints are relevant in the context of quark matter at the interior of compact stars. We analyze the implications of color superconductivity on compact star configurations using different hadronic and quark equations of state.Presented at the 15th Indian-Summer School of Physics: Understanding Dense Matter, Prague, Czech Republic, 27 August–1 September, 2003.     

Quark deconfinement in neutron star cores

Whether or not the deconfined quark phase exists in neutron star cores is an open question. We use two realistic effective quark models, the three-flavor Nambu-Jona-Lasinio model and the modified quark-meson coupling model, to describe the neutron star matter. We show that the modified quark-meson coupling model, which is fixed by reproducing the saturation properties of nuclear matter, can be consistent with the experimental constraints from nuclear collisions. After constructing possible hybrid equations of state (EOSes) with an unpaired or color superconducting quark phase with the assumption of the sharp hadron-quark phase transition, we discuss the observational constraints from neutron stars on the EOSes. It is found that the neutron star with pure quark matter core is unstable and the hadronic phase with hyperons is denied, while hybrid EOSes with a two-flavor color superconducting phase or unpaired quark matter phase are both allowed by the tight and most reliable constraints from two stars Ter 5 I and EXO 0748-676. And the hybrid EOS with an unpaired quark matter phase is allowed even compared with the tightest constraint from the most massive pulsar star PSR J0751+1807.     

Model of an exotic chiral superconducting phase in a graphene bilayer

We theoretically demonstrate the formation of a new type of unconventional superconductivity in graphene materials, which exhibits a gapless property. The studied superconductivity is based on an interlayer pairing of chiral electrons in bilayer graphene, which results in an exotic s-wave spin-triplet condensate order with anomalous thermodynamic properties. These include the possibility of a temperature-induced condensation causing an increase of the pairing gap with increasing temperature and an entropy of the stable superconducting state which can be higher than its value in the normal state. Our study reveals the analogy of the interlayer superconductivity in graphene materials to the color superconductivity in dense quark matter and the gapless pairing states in nuclear matter and ultracold atomic gases.     

Theoretical investigation of the superconducting gaps in the Fe-based superconductors

Based on an antiferromagnetic (AFM) spin fluctuation approximation, we study the superconducting gaps in Fe-based compound using two-band model. We find that our results are consistent with the previous work that concludes sign-reversal extended s-wave pairings between different Fermi surface sheets. The different superconducting gap magnitude around different Fermi surface sheets is probably due to the different density of states on them. This calculation can give insight to the recent angle-resolved photoemission (ARPES) experiments on these materials. To detect the phase variation of the superconducting gap over the Fermi surfaces, we propose a new method for measuring the particular wave vector phonon linewidth. In the case of the sign-reversal superconducting pairing, the linewidth shows continuities compared to the case of no phase variation.     

Editorial

Many excellent articles and textbooks on superconductivity have been published. However, concise and easily-handled data books written for scientists and engineers who work in the field of superconducting materials are very few. This article aims to collect and outline basic properties of superconducting materials and to provide such people with a database. The properties listed include crystal and electronic structures, equilibrium phase diagram, superconducting critical temperature, critical magnetic fields, critical current density, pinning force, specific heat coefficient, Debye temperature, penetration depth, coherence length, GL parameter, energy gap, electronic density of states at the Fermi level, electron-phonon coupling constant, Coulomb pseudopotential, and others. Emphasis is on the materials used in superconductive applications. Structural phase transitions such as martensitic transformations and transitions to the charge-density-wave state in superconducting materials are also reviewed. The properties of superconducting oxides will be summarized in the next article of this series.     

量子色动力学在有限温度密度区间的相结构

本文综述量子色动力学在有限温度密度区间的相结构,包括高密条件下的色超导态和在高温条件下相对论重离子碰撞实验中产生的强耦合夸克-胶子等离子体。我们简要地介绍在相对论重离子碰撞实验中发现强耦合夸克-胶子等离子体的历史,并且讨论用体粘滞系数与熵的比值确定QCD临界点的可能性。对于在高密区域的相结构,我们着重讨论错位配对情况下的非标准色超导态,解释无能隙色超导态的色磁不稳定性、Sarma不稳定性和Higgs不稳定性.     

量子色动力学在有限温度密度区间的相结构(英文)

本文综述量子色动力学在有限温度密度区间的相结构,包括高密条件下的色超导态和在高温条件下相对论重离子碰撞实验中产生的强耦合夸克-胶子等离子体。我们简要地介绍在相对论重离子碰撞实验中发现强耦合夸克-胶子等离子体的历史,并且讨论用体粘滞系数与熵的比值确定QCD临界点的可能性。对于在高密区域的相结构,我们着重讨论错位配对情况下的非标准色超导态,解释无能隙色超导态的色磁不稳定性、Sarma不稳定性和Higgs不稳定性.     

Effect of pairing correlation on low-lying quadrupole states in Sn isotopes

We examined the low-lying quadrupole states in Sn isotopes in the framework of fully self-consistent Hartree-Fock+BCS plus QRPA.We focus on the effect of the density-dependence of pairing interaction on the properties of the low-lying quadrupole state.The SLy5 Skyrme interaction with surface,mixed,and volume pairings is employed in the calculations,respectively.We find that the excitation energies and the corresponding reduced electric transition probabilities of the first 2~+ state are different,given by the three pairing interactions.The properties of the quasiparticle state,two-quasiparticle excitation energy,reduced transition amplitude,and transition densities in~(112)Sn are analyzed in detail.Two different mechanisms,the static and dynamical effects,of the pairing correlation are also discussed.The results show that the surface,mixed,and volume pairings indeed affect the properties of the first 2~+ state in the Sn isotopes.