Nonlinear sigma model approach for phase disorder transitions and the pseudogap phase in chiral Gross-Neveu, Nambu-Jona-Lasinio models and strong-coupling superconductors

We briefly review the nonlinear sigma model approach for the subject of increasing interest: "two-step" phase transitions in the Gross-Neveu and the modified Nambu-Jona-Lasinio models at low $N$ and condensation from pseudogap phase in strong-coupling superconductors. Recent success in describing "Bose-type" superconductors that possess two characterstic temperatures and a pseudogap above $T_c$ is the development approximately comparable with the BCS theory. One can expect that it should have influence on high-energy physics, similar to impact of the BCS theory on this subject. Although first generalizations of this concept to particle physics were made recently, these results were not systematized. In this review we summarize this development and discuss similarities and differences of the appearence of the pseudogap phase in superconductors and the Gross-Neveu and Nambu-Jona-Lasinio - like models. We discuss its possible relevance for chiral phase transition in QCD and color superconductors. This paper is organized in three parts: in the first section we briefly review the separation of temperatures of pair formation and pair condensation in strong - coupling and low carrier density superconductors (i.e. the formation of the {\it pseudogap phase}). Second part is a review of nonlinear sigma model approach to an analogous phenomenon in the Chiral Gross-Neveu model at small N. In the third section we discuss the modified Nambu-Jona-Lasinio model where the chiral phase transition is accompanied by a formation of a phase analogous to the pseudogap phase.Comment: A brief review. Replaced with journal version (some grammatical corrections). The latest updates of this and related papers are also available at the author home page http://www.teorfys.uu.se/PEOPLE/egor

Thermodynamics of Crossover from Weak- to Strong-Coupling Superconductivity

In this paper we study an evolution of low-temperature thermodynamical quantities for an electron gas with a $\delta$-function attraction as the system crosses over from weak-coupling (BCS-type) to strong-coupling (Bose-type) superconductivity in three and two dimensions.Comment: Replaced with journal version. Insignificant presentation changes. Links to related papers are also available at the author home page http://www.teorfys.uu.se/PEOPLE/egor

Dual neutral variables and knot solitons in triplet superconductors

In this paper we derive a dual presentation of free energy functional for spin-triplet superconductors in terms of gauge-invariant variables. The resulting equivalent model in ferromagnetic phase has a form of a version of the Faddeev model. This allows one in particular to conclude that spin-triplet superconductors allow formation of stable finite-length closed vortices (the knotted solitons).Comment: Replaced with version published in PRL (added a discussion of the effect of the coupling of the fields {\vec s} and {\vec C} on knot stability). Latest updates of the paper and miscellaneous links related to knotted solitons are also available at the homepage of the author http://www.teorfys.uu.se/PEOPLE/egor/ . Animations of knotted solitons by Hietarinta and Salo are available at http://users.utu.fi/h/hietarin/knots/c45_p2.mp

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

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 short-range 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.Comment: in print in Phys. Rev. B Rapid Communications. v2: presentation is made more accessible for a general reader. Latest updates and links to related papers are available at the home page of one of the authors: http://people.ccmr.cornell.edu/~egor

Characteristic length scales and formation of vortices in the Abelian Higgs model in the presence of a uniform background charge

In this brief report we consider a non-local Abelian Higgs model in the presence of a neutralizing uniform background charge. We show that such a system possesses vortices which key feature is a strong radial electric field. We estimate the basic properties of such an object and characteristic length scales in this model.Comment: Replaced with journal version. Some minor change

Unusual states of vortex matter in mixtures of Bose--Einstein Condensates on rotating optical lattices

A striking property of a single-component superfluid under rotation, is that a broken symmetry in the order parameter results in a broken translational symmetry, a vortex lattice. If translational symmetry is restored, the phase of the order parameter disorders and the broken symmetry in the order parameter is restored. We show that for Bose-Condensate mixtures on optical lattices (which may possess a negative dissipationless intercomponent drag), a new situation arises. A phase disordered nonsuperfluid component can break translational symmetry in response to rotation due to interaction with a superfluid component. This state is a modulated vortex liquid which breaks translational symmetry in the direction transverse to the rotation vector.Comment: 4 pages, 3 figures. To be published in Physical Review Letter

Frontiers, challenges, and solutions in modeling of swift heavy ion effects in materials

Since a few breakthroughs in the fundamental understanding of the effects of swift heavy ions (SHI) decelerating in the electronic stopping regime in the matter have been achieved in the last decade, it motivated us to review the state-of-the-art approaches in the modeling of SHI effects. The SHI track kinetics occurs via several well-separated stages: from attoseconds in ion-impact ionization depositing energy in a target, to femtoseconds of electron transport and hole cascades, to picoseconds of lattice excitation and response, to nanoseconds of atomic relaxation, and even longer macroscopic reaction. Each stage requires its own approaches for quantitative description. We discuss that understanding the links between the stages makes it possible to describe the entire track kinetics within a multiscale model without fitting procedures. The review focuses on the underlying physical mechanisms of each process, the dominant effects they produce, and the limitations of the existing approaches as well as various numerical techniques implementing these models. It provides an overview of ab-initio-based modeling of the evolution of the electronic properties; Monte Carlo simulations of nonequilibrium electronic transport; molecular dynamics modeling of atomic reaction on the surface and in the bulk; kinetic Mote Carlo of atomic defect kinetics; finite-difference methods of tracks interaction with chemical solvents describing etching kinetics. We outline the modern methods that couple these approaches into multiscale multidisciplinary models and point to their bottlenecks, strengths, and weaknesses. The analysis is accompanied by examples of important results improving the understanding of track formation in various materials. Summarizing the most recent advances in the field of the track formation process, the review delivers a comprehensive picture and detailed understanding of the phenomena.Comment: to be submitte

Revised Phase Diagram of the Gross-Neveu Model

We confirm earlier hints that the conventional phase diagram of the discrete chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical potential. We present the corrected phase diagram constructed in mean field theory. It has three different phases, including a kink-antikink crystal phase. All transitions are second order. The driving mechanism for the new structure of baryonic matter in the Gross-Neveu model is an Overhauser type instability with gap formation at the Fermi surface.Comment: Revtex, 12 pages, 15 figures; v2: Axis labelling in Fig. 9 correcte

Possible Pseudogap Phase in QCD

Thermal pion fluctuations, in principle, can completely disorder the phase of the quark condensate and thus restore chiral symmetry. If this happens before the quark condensate melts, strongly-interacting matter will be in the pseudogap state just above the chiral phase transition. The quark condensate does not vanish locally and quarks acquire constituent masses in the pseudogap phase, despite chiral symmetry is restored.Comment: 8 pages, 1 figure; v2: references added; v3: argumerts modified; v4: minor changes; v5: a misprint correcte

Superconductivity in the quasi-two-dimensional Hubbard model

On the basis of spin and pairing fluctuation-exchange approximation, we study the superconductivity in quasi-two-dimensional Hubbard model. The integral equations for the Green's function are self-consistently solved by numerical calculation. Solutions for the order parameter, London penetration depth, density of states, and transition temperature are obtained. Some of the results are compared with the experiments for the cuprate high-temperature superconductors. Numerical techniques are presented in details. With these techniques, the amount of numerical computation can be greatly reduced.Comment: 17 pages, 13 figure