Crossover from BCS to Composite Boson (Local Pair) Superconductivity in Quasi-2D systems

The crossover from cooperative Cooper pairing to independent bound state (composite bosons) formation and condensation in quasi-2D systems is studied. It is shown that at low carrier density the critical superconducting temperature is equal to the temperature of Bose-condensation of ideal quasi-2D Bose-gas with heavy dynamical mass, meanwhile at high densities the BCS result remains valid. The evident nonmonotoneous behaviour of the critical temperature as function of the coupling constant (the energy of the two particle bound state) is a qualitative difference of quasi-2D crossover from 3D one.Comment: 9 pages, LaTeX, no figures. (The latest version which appeared in the journal

Nondecoupling phenomena in QED in a magnetic field and noncommutative QED

The dynamics in QED in a strong constant magnetic field and its connection with the noncommutative QED are studied. It is shown that in the regime with the lowest Landau level (LLL) dominance the U(1) gauge symmetry in the fermion determinant is transformed into the noncommutative $U(1)_{nc}$ gauge symmetry. In this regime, the effective action is intimately connected with that in noncommutative QED and the original U(1) gauge Ward identities are broken (the LLL anomaly). On the other hand, it is shown that although a contribution of each of an infinite number of higher Landau levels is suppressed in an infrared region, their cumulative contribution is not (a nondecoupling phenomenon). This leads to a restoration of the original U(1) gauge symmetry in the infrared dynamics. The physics underlying this phenomenon reflects the important role of a boundary dynamics at spatial infinity in this problem.Comment: 7 pages, REVTeX

Excitonic Instability and Gap Generation in Monolayer Graphene

We analyze the excitonic instability in graphene by solving the Bethe–Salpeter equation for the electron-hole bound state. In the supercritical regime, we show that this equation has a tachyon in its spectrum. We argue that the excitonic instability is resolved through the formation of an electron-hole condensate leading to the gap (mass) generation in the quasiparticle spectrum. Such a gap could be observed in a free standing clean graphene.За допомогою рiвняння Бете–Солпiтера для електрон-дiркового зв’язаного стану дослiджено проблему екситонної нестабiльностi в графенi. Показано, що для надкритичної константи зв’язку спектр має тахiоннi розв’язки. Екситонна нестабiльнiсть приводить до формування електрон-дiркового конденсату та щiлини у спектрi квазiчастинок. Ця щiлина може бути спостережена у графенi без домiшок

Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field

We study symmetry breaking and gap generation for fermions in the 2D space of constant negative curvature (the Lobachevsky plane) in an external covariantly constant magnetic field in a four-fermion model. It is shown that due to the magnetic and negative curvature catalysis phenomena the critical coupling constant is zero and there is a symmetry breaking condensate in the chiral limit even in free theory. We analyze solutions of the gap equation in the cases of zero, weak, and strong magnetic fields. As a byproduct we calculate the density of states and the Hall conductivity for noninteracting fermions that may be relevant for studies of graphene.Comment: 12 pages, no figure

Gap generation and flat band catalysis in dice model with local interaction

Theoretical Physic

Toward theory of quantum Hall effect in graphene

We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic catalysis dynamics necessarily coexist (the latter have the form of Dirac masses and correspond to excitonic condensates). This feature of graphene could lead to important consequences, in particular, for the existence of gapless edge states. Solutions of the gap equation corresponding to recently experimentally discovered novel plateaus in graphene in strong magnetic fields are described

Effect of next-to-nearest neighbor hopping on electronic properties of graphene

In the tight-binding approximation, we take into account the next-to-nearest neighbor hopping in graphene that leads to nonrelativistic-like corrections in its low energy spectrum. The electronic density of states in a magnetic field is found and the fan diagram is plotted, which interpolates between those for the relativistic and nonrelativistic limiting cases. It is shown that the Berry phase for the system under consideration coincides exactly with its value for the relativistic system

On Chiral Symmetry Breaking in a Constant Magnetic Field in Higher Dimension

Chiral symmetry breaking in the Nambu-Jona-Lasinio model in a constant magnetic field is studied in spacetimes of dimension D > 4. It is shown that a constant magnetic field can be characterized by [(D-1)/2] parameters. For the maximal number of nonzero field parameters, we show that there is an effective reduction of the spacetime dimension for fermions in the infrared region D $\to$ 1 + 1 for even-dimensional spacetimes and D $\to$ 0 + 1 for odd-dimensional spacetimes. Explicit solutions of the gap equation confirm our conclusions.Comment: 11 pages, LaTe

On the Effective Potential for Local Composite Operators

We show that the effective potential for local composite operators is a useful object in studing dynamical symmetry breaking by calculating the effective potential for the local composite operators $\bar{\psi} \psi$ and $\phi^2$ in the Gross-Neveu (GN) and O(N) models, respectively. Since the effective potential for local composite operators can be calculated by using the Cornwall-Jackiw-Tomboulis (CJT) effective potential in theory with additional bare mass terms, we show that divergences in the effective potential for local composite operators are the same as in the CJT effective potential. We compare the results obtained with the results give by the auxiliary field method.Comment: 17 pages, LaTeX, the analysis of the O(N) model with finite cut-off have been reconsidered and the corresponding important reference have been adde

Gluonic phase in neutral two-flavor dense QCD

In the Ginzburg-Landau approach, we describe a new phase in neutral two-flavor quark matter in which gluonic degrees of freedom play a crucial role. We call it a gluonic phase. In this phase gluonic dynamics cure a chromomagnetic instability in the 2SC solution and lead to spontaneous breakdown of the color gauge symmetry, the electromagnetic U(1), and the rotational SO(3). In other words, the gluonic phase describes an anisotropic medium in which the color and electric superconductivities coexist. Because most of the initial symmetries in this system are spontaneously broken, its dynamics is very rich.Comment: Revtex4, 11 pages, clarifications and new section added, references added, to appear in Phys. Lett.