Superfluid phases of quark matter. III. Supercurrents and vortices

Iida, Kei; Baym, Gordon

doi:10.1103/physrevd.66.014015

Cited by 102 publications

(182 citation statements)

References 39 publications

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“…Transverse excitations will be ignored in the present study, but play a role in breaking up phase coherence in the superfluid state and hence are relevant for responses to magnetic field and rotation [9,13] and for reduction in the transition temperature [14].…”

Section: Introductionmentioning

confidence: 99%

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Collective excitations in a superfluid of color-flavor locked quark matter

Fukushima

Iida

2005

Phys. Rev. D

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We investigate collective excitations coupled with baryon density in a system of massless threeflavor quarks in the collisionless regime. By using the Nambu-Jona-Lasinio (NJL) model in the mean-field approximation, we field-theoretically derive the spectra both for the normal and colorflavor locked (CFL) superfluid phases at zero temperature. In the normal phase, we obtain usual zero sound as a low-lying collective mode in the particle-hole (vector) channel. In the CFL phase, the nature of collective excitations varies in a way dependent on whether the excitation energy, ω, is larger or smaller than the threshold given by twice the pairing gap ∆, at which pair excitations with nonzero total momentum become allowed to break up into two quasiparticles. For ω ≪ 2∆, a phonon corresponding to fluctuations in the U (1) phase of ∆ appears as a sharp peak in the particle-particle ("H") channel. We reproduce the property known from low energy effective theories that this mode propagates at a velocity of vH = 1/ √ 3 in the low momentum regime; the decay constant fH obtained in the NJL model is identical with the QCD result obtained in the mean-field approximation. We also find that as the momentum of the phonon increases, the excitation energy goes up and asymptotically approaches ω = 2∆. Above the threshold for pair excitations (ω > 2∆), zero sound manifests itself in the vector channel. By locating the zero sound pole of the vector propagator in the complex energy plane we investigate the attenuation and energy dispersion relation of zero sound. In the long wavelength limit, the phonon mode, the only low-lying excitation, has its spectral weight in the H channel alone, while the spectral function vanishes in the vector channel. This is due to nontrivial mixing between the H and vector channels in the superfluid medium. We finally extend our study to the case of nonzero temperature. We demonstrate how Landau damping smears the phonon peak in the finite temperature spectral function. We find a pure imaginary pole of the H propagator in the complex energy plane, which can be identified as a diffusive mode responsible for the Landau damping. From the pole position we derive the thermal diffusion constant.

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Section: Introductionmentioning

confidence: 99%

“…In fact, the ground state of liquid 3 He, i.e., the B phase, has a condensate isotropic in spin-orbit space, which is similar to the CFL phase in which the condensate is isotropic in color-flavor space. In both systems, responses to rotation are characterized by a lattice of vortices [9].…”

Section: Introductionmentioning

confidence: 99%

Collective excitations in a superfluid of color-flavor locked quark matter

Fukushima

Iida

2005

Phys. Rev. D

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“…The properties of color superconductors have been studied so far in the weak coupling regime with onegluon exchange between quarks [2,3], in the strong coupling regime with an effective four-fermion interaction [4], in Ginzburg-Landau (GL) theory [5,6], and from the perspective of sum rules and phenomenological equations [7]. A major difference of color superconductors and metallic superconductors is that the former is a highly relativistic system in which the long-range magnetic interaction (dynamically screened only by Landau damping [8]) is responsible for the formation of the superconducting gap.…”

Section: Introductionmentioning

confidence: 99%

Thermal fluctuations of gauge fields and first order phase transitions in color superconductivity

et al. 2004

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We study the effects of thermal fluctuations of gluons and the diquark pairing field on the superconducting-to-normal state phase transition in a three-flavor color superconductor, using the Ginzburg-Landau free energy. At high baryon densities, where the system is a type I superconductor, gluonic fluctuations, which dominate over diquark fluctuations, induce a cubic term in the Ginzburg-Landau free energy, as well as large corrections to quadratic and quartic terms of the order parameter. The cubic term leads to a relatively strong first order transition, in contrast with the very weak first order transitions in metallic type I superconductors. The strength of the first order transition decreases with increasing baryon density. In addition gluonic fluctuations lower the critical temperature of the first order transition. We derive explicit formulas for the critical temperature and the discontinuity of the order parameter at the critical point. The validity of the first order transition obtained in the one-loop approximation is also examined by estimating the size of the critical region.

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“…Another candidate for this type of superconductivity is the projected liquid metallic state of hydrogen [10] where this regime is expected to be realized under certain conditions. A similar situation might also occur in the color superconducting state in quark matter [11]. Certain features of the considered state should be preserved and might be experimentally accessed for vortex stacks [18] in layered systems when one layer is type-II and another is strongly type-I.…”

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confidence: 99%

“…Recently, multicomponent superconducting systems have attracted increasing interest in areas ranging through metallic superconductors, hydrogen in extreme conditions and color superconductivity in dense QCD [9,10,11]. Below we consider a generic two-component superconductor (TCS), showing that it allows a novel type of thermodynamically stable vortices, whose electrodynamics is of Pippard type with respect to one of the order parameters and which have non-monotonic interaction energy for a wide range of parameters as an intrinsic feature.…”

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Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors

2005

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Traditionally, superconductors are categorized as type-I or type-II. Type-I superconductors support only Meissner and normal states, while type-II superconductors form magnetic vortices in sufficiently strong applied magnetic fields. Recently there has been much interest in superconducting systems with several species of condensates, in fields ranging from Condensed Matter to High Energy Physics. Here we show that the type-I/type-II classification is insufficient for such multicomponent superconductors. We obtain solutions representing thermodynamically stable vortices with properties falling outside the usual type-I/type-II dichotomy, in that they have the following features: (i) Pippard electrodynamics, (ii) interaction potential with long-range attractive and shortrange repulsive parts, (iii) for an n-quantum vortex, a non-monotonic ratio E(n)/n where E(n) is the energy per unit length, (iv) energetic preference for non-axisymmetric vortex states, "vortex molecules". Consequently, these superconductors exhibit an emerging first order transition into a "semi-Meissner" state, an inhomogeneous state comprising a mixture of domains of two-component Meissner state and vortex clusters.The formation of vortices in type-II superconductors subjected to a magnetic field is one of the most remarkable phenomena occuring in condensed matter. In all type-II superconductors (i.e. superconductors where the GL parameter, which is the ratio of the magentic field penetration length to the coherence lenth, is κ > 1/ √ 2 [1]) these vortices share a set of properties: an n-quantum vortex is unstable with respect to decay into n onequantum vortices, two vortices have purely repulsive interaction, and invasion of vortices under normal conditions is a second order phase transition characterised by a critical value of the external magnetic field H c1 .Vortices as solutions of the GL equations also exist formally in a type-I superconductor (κ < 1/ √ 2), but these vortices are thermodynamically unstable. The special case κ = 1/ √ 2 is also very interesting since, at this value of κ, vortices do not interact [2,3]. One should note, however, that in real life systems the situation is more complicated; experiments [4] show that in certain materials with κ ≈ 1/ √ 2 there might exist a tiny attractive force between vortices at a certain distance. Such an interaction was reproduced in a modified one-component GL model with additional terms in the regime κ ≈ 1/ √ 2 [5]. We should also mention a long range van der Waals -type vortex attraction in layered systems produced by thermal fluctuations or disorder [6].Besides superconductivity, the vortex concept has a direct counterpart in High Energy Physics, called the Nielsen-Olesen string. Such strings have been considered in cosmology [7] where they are expected to form during a symmetry breaking phase transition in the early universe. There also exists a similar type-I/type-II division of semilocal cosmic strings in the Higgs doublet model [8].Recently, multicomponent superconducting systems hav...

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Superfluid phases of quark matter. III. Supercurrents and vortices

Cited by 102 publications

References 39 publications

Collective excitations in a superfluid of color-flavor locked quark matter

Collective excitations in a superfluid of color-flavor locked quark matter

Thermal fluctuations of gauge fields and first order phase transitions in color superconductivity

Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors

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