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V. Ch. Zhukovsky

Publications and source records attributed to V. Ch. Zhukovsky.

At least 19 recordsLinked to original sources
arXiv2016

Graphene under the influence of Aharonov-Bohm flux and constant magnetic field

Investigation of real two-dimensional systems with Dirac-like electronic behavior under the influence of magnetic field is challenging and leads to many interesting physical results. In this paper we study 2D graphene model with a particular form of magnetic field as a superposition of a homogeneous field and an Aharonov-Bohm vortex. For this configuration, electronic wave functions and energy spectrum were obtained and it was shown that the magnetic Aharonov-Bohm vortex plays the role of a charge impurity. As a demonstration of vacuum properties of the system, vacuum current, as well as an electric current, is calculated and their representation for particular limiting cases of magnetic field is obtained.

cond-mat.mes-hall↗
arXiv2016

Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions

In this paper we consider a class of (2+1)D schematic models with four-fermion interactions that are effectively used in studying condensed-matter systems with planar crystal structure, and especially graphene. Symmetry breaking in these models occurs due to a possible appearance of condensates. Special attention is paid to the symmetry properties of the appearing condensates in the framework of discrete chiral and $\mathcal C$, $\mathcal P$ and $\mathcal T$ transformations. Moreover, boundary conditions corresponding to carbon nanotubes are considered and their relations with the effect of an applied external magnetic field are studied. To this end we calculated the effective potential for the nanotube model including effects of finite temperature, density and an external magnetic field. As an illustration we made numerical calculations of the chiral symmetry properties in a simpler Gross--Neveu model with only one condensate taken into account. We also investigated the phase structure of the nanotube model under the influence of the Aharonov--Bohm effect and demonstrated that there is a nontrivial relation between the magnitude of the Aharonov--Bohm phase, compactification of the spatial dimension and thermal restoration of the originally broken chiral symmetry.

cond-mat.mes-hall↗
arXiv2014

Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in the NJL$_2$ model

We investigate the possibility of spatially homogeneous and inhomogeneous chiral fermion-antifermion condensation and superconducting fermion-fermion pairing in the (1+1)-dimensional model by Chodos {\it et al.} [ Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature $T$, electric charge chemical potential $μ$ and chiral charge chemical potential $μ_5$. It is shown that at $G_1 G_2$ (called duality correspondence). Under the duality transformation the (inhomogeneous) chiral symmetry breaking (CSB) phase is mapped into the (inhomogeneous) superconducting (SC) phase and vice versa. If $G_1=G_2$, then the phase structure of the model is self-dual. Nevertheless, the degeneracy between the CSB and SC phases is possible in this case only when there is a spatial inhomogeneity of condensates.

hep-th↗
arXiv2013

Suppression of superconductivity by inhomogeneous chiral condensation in the NJL$_2$ model

We investigate the possibility of spatially inhomogeneous chiral and Cooper, or superconducting, pairing in the (1+1)-dimensional model by Chodos et al [ Phys. Rev. D61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero temperature $T$ and quark number chemical potential $μ$. It is shown in the framework of the Fulde--Ferrel inhomogeneity ansatz for chiral and Cooper condensates that if $G_1>G_2$, where $G_1$ and $G_2$ are the coupling constants in the quark-antiquark and diquark channels, then in the $(μ,T)$-phase diagram the superconducting phase is suppressed by spatially inhomogeneous chiral spiral phase with broken chiral symmetry. In contrast, in the above mentioned original Chodos et al model, where only the opportunity for homogeneous condensates were taken into account, the superconducting phase is realized at sufficiently high values of $μ$ at arbitrary values of $G_2>0$, including the interval $0<G_2<G_1$.

hep-th↗
arXiv2013

Pseudopotential model for Dirac electrons in graphene with line defects

We consider electron transport in a planar fermion model containing various types of line defects modelled by $δ$--function pseudopotentials with different matrix coefficients. The transmission probability for electron transport through the defect line is obtained for various types of pseudopotentials. For the schematic model considered that may describe a graphene structure with different types of linear defects, the valley polarization is obtained.

cond-mat.mes-hall↗
arXiv2013

Superconductivity phenomenon induced by external in-plane magnetic field in (2+1)-dimensional Gross--Neveu type model

Phase structure of the (2+1)-dimensional model with four-fermion interaction of spin-1/2 quasiparticles (electrons) both in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting) channels is considered at nonzero chemical potential $μ$ and under the influence of an in-plane, i.e. parallel to a system sheet, external magnetic field $\vec B_\parallel$. It is shown that at sufficiently large values of $μ$ and/or $\vec B_\parallel$ the Cooper pairing (or superconducting) phase appears in the system at arbitrary relation between coupling constants, provided that there is an (arbitrary small) attractive interaction in the superconducting channel. In particular, at sufficiently weak attractive interaction in the chiral channel, the Cooper pairing occurs even at infinitesimal values of $μ$ and/or $\vec B_\parallel$. The superconducting phase of the model is always a paramagnetic one.

hep-th↗
arXiv2012

Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory

In the paper a generalization of the (1+1)-dimensional model by Chodos et al [Phys. Rev. D61, 045011 (2000)] has been performed to the case of (2+1)-dimensional spacetime. The model includes four-fermion interaction both in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting) channels. We study temperature $T$ and chemical potential $μ$ induced phase transitions in the leading order of large-$N$ expansion technique, where $N$ is a number of fermion fields. It is shown that at sufficiently large values of $μ$ and arbitrary relations between coupling constants, superconducting phase appears in the system both at T=0 and $T>0$. In particular, at T=0 and sufficiently weak attractive interaction in the chiral channel, the Cooper pairing occurs for arbitrary couplings in the superconducting channel even at infinitesimal values of $μ$.

hep-th↗
arXiv2012

Inhomogeneous charged pion condensation phenomenon in the NJL$_2$ model with quark number and isospin chemical potentials

The properties of two-flavored massive Nambu--Jona-Lasinio model in (1+1)-dimensional spacetime are investigated in the presence of isospin and quark number chemical potentials. The consideration is performed in the large-$N_c$ limit, where $N_c$ is the number of colored quarks. It is shown in the framework of this model that charged pion condensation phenomenon of dense quark/hadron isotopically asymmetric matter is rather a spatially inhomogeneous than a homogeneous one.

hep-ph↗
arXiv2011

Chiral density waves in the NJL$_2$ model with quark number and isospin chemical potentials

We investigate the phase portrait of the (1+1)-dimensional massless two-flavored NJL$_2$ model containing a quark number chemical potential $μ$ and an isospin chemical potential $μ_I$ in the limit of a large number of colors $N_c\to\infty$. Particular attention is paid to the question to what extent the inclusion of an isospin asymmetry affects chiral condensates to have a spatial inhomogeneity in the form of the so-called chiral density waves (CDW) (chiral spirals). It is shown that at zero temperature and comparatively small values of $μ$, i.e. at $μ<μ_c\approx 0.68M_0$ ($M_0$ is the dynamical quark mass in the vacuum) only the homogeneous charged pion condensation phase is realized for arbitrary nonzero values of $μ_I$. Contrary to this, for large values of $μ>μ_c$, two CDW phases appear in the $(μ_I,μ)$-phase diagram of the model. In the first phase, CDWs are clockwise twisted chiral spirals and in the second phase they are counterclockwise. The influence of nonzero temperature on the formation of the CDW phases is also investigated.

hep-ph↗
arXiv2011

Finite-size effects in pion condensation phenomena of dense baryonic matter in the NJL$_2$ model

The properties of two-flavored massless Nambu-Jona-Lasinio model in (1+1)-dimensional $R^1\times S^1$ spacetime with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials $μ_I$, $μ$. The consideration is performed in the large $N_c$ limit, where $N_c$ is the number of colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the circumference $S^1$) the pion condensation (PC) phase with {\it zero quark number density} is realized at arbitrary nonzero $μ_I$ and for rather small values of $μ$. However, at arbitrary finite values of $L$ the phase portrait of the model contains the PC phase with {\it nonzero quark number density} (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of $L$.

hep-ph↗
arXiv2010

Chiral density waves in quark matter within the Nambu--Jona-Lasinio model in an external magnetic field

A possibility of formation of static dual scalar and pseudoscalar density wave condensates in dense quark matter is considered for the Nambu--Jona-Lasinio model in an external magnetic field. Within a mean-field approximation, the effective potential of the theory is obtained and its minima are numerically studied; a phase diagram of the system is constructed. It is shown that the presence of a magnetic field favors the formation of spatially inhomogeneous condensate configurations at low temperatures and arbitrary non-zero values of the chemical potential.

hep-ph↗
arXiv2010

Dynamical Fermion Masses Under the Influence of Kaluza-Klein Fermions and a Bulk Abelian Gauge Field

The dynamical fermion mass generation on a 3-brane in the 5D space-time is discussed in a model with bulk fermions in interaction with fermions on the brane assuming the presence of a constant abelian gauge field component $A_5$ in the bulk. We calculate the effective potential as a function of the fermion masses and the gauge field component $A_5$. The masses can be found from the stationarity condition for the effective potential (the gap equation). We formulate the equation for the mass spectrum of the 4D--fermions. The phases with finite and vanishing fermion masses are studied and the dependence of the masses on the radius of the 5th dimension is analyzed. The influence of the $A_5$-component of the gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable. The critical values of the $A_5$ field, the coupling constant and the radius are examined.

hep-th↗
arXiv2009

Casimir effect within D=3+1 Maxwell-Chern-Simons electrodynamics

Within the framework of the (3+1)-dimensional Lorentz-violating extended electrodynamics including the CPT-odd Chern-Simons term, we consider the electromagnetic field between the two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. We also show that the tachyon-induced vacuum instability vanishes when the separation between the plates is sufficiently small though finite. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over all one-particle eigenstate energies using the two different methods, the zeta function technique and the transformation of the discrete sum into a complex plane integral via the residue theorem. The resulting correction to the Casimir force, which is attractive and quadratic in the Chern-Simons term, disagrees with the one calculated in [M.Frank and I.Turan, Phys.Rev.D 74, 033016(2006)], using the misinterpreted equations of motion. Compared to the experimental data, our result places a constraint on the absolute value of the Chern-Simons term.

hep-th↗
arXiv2009

Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space

We study the dynamical breaking of chiral and color symmetries of dense quark matter in the ultrastatic hyperbolic spacetime $R\otimes H^3$ in the framework of an extended Nambu--Jona-Lasinio model. On the basis of analytical expressions for chiral and color condensates as functions of curvature and temperature, the phenomenon of dimensional reduction and gravitational catalysis of symmetry breaking in strong gravitational field is demonstrated in the regime of weak coupling constants. In the case of strong couplings it is shown that curvature leads to small corrections to the flat-space values of condensate and thus enhances the symmetry breaking effects. Finally, using numerical calculations phase transitions under the influence of chemical potential and negative curvature are considered and the phase portrait of the system is constructed.

hep-th↗
arXiv2008

Finite size effects in the Gross-Neveu model with isospin chemical potential

The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional $R^1\times S^1$ spacetime with compactified space coordinate are investigated in the presence of the isospin chemical potential $μ_I$. The consideration is performed in the limit $N_c\to\infty$, i.e. in the case with infinite number of colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the circumference $S^1$) the pion condensation phase is realized for arbitrary small nonzero $μ_I$. At finite values of $L$, the phase portraits of the model in terms of parameters $ν\simμ_I$ and $λ\sim 1/L$ are obtained both for periodic and antiperiodic boundary conditions of the quark field. It turns out that in the plane $(λ,ν)$ there is a strip $0\leλ<λ_c$ which lies as a whole inside the pion condensed phase. In this phase the pion condensation gap is an oscillating function vs both $λ$ (at fixed $ν$) and $ν$ (at fixed $λ$).

hep-ph↗
arXiv2008

Pion condensation of quark matter in the static Einstein universe

In the framework of an extended Nambu--Jona-Lasinio model we are studying pion condensation in quark matter with an asymmetric isospin composition in a gravitational field of the static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates and to point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is shortly discussed.

hep-ph↗
arXiv2007

CPT and Lorentz violation effects in hydrogen-like atoms

Within the framework of Lorentz-violating extended electrodynamics, the Dirac equation for a bound electron in an external electromagnetic field is considered assuming the interaction with a CPT-odd axial vector background $b_μ$. The quasi-relativistic Hamiltonian is obtained using a $1/c$-series expansion. Relativistic Dirac eigenstates in a spherically-symmetric potential are found accurate up to the second order in $b_0$. $b_0$-induced CPT-odd corrections to the electromagnetic dipole moment operators of a bound electron are calculated that contribute to the anapole moment of the atomic orbital and may cause a specific asymmetry of the angular distribution of the radiation of a hydrogen atom.

hep-th↗