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Radiative corrections which remove accidental degeneracy in the spectrum of the relativistic hydrogen atom and lead to the modification of the Coulomb law, are calculated within the novel approach, based on the exact solution of the Dirac equation with the Coulomb potential. The energy spectrum of the hydrogen atom is obtained with account of these corrections and the Lamb shift is calculated for the lowest energy states., Comment: 24 pages

We consider electronic spectra of graphene nanotubes and their perturbation by impurity atoms absorbed at different positions on nanotube surfaces, within the framework of Anderson hybrid model. A special attention is given to the cases when Dirac-like 1D modes appear in the nanotube spectrum and their hybridization with localized impurity states produces, at growing impurity concentration $c$, onset of a mobility gap near the impurity level and even opening, at yet higher $c$, of some narrow delocalized range within this mobility gap. Such behaviors are compared with the similar effects in the previously studied 2D graphene and armchair type graphene nanoribbons. Some possible practical applications are discussed., Comment: 14 pages, 17 figures

We present an X-ray spectro-polarimetric analysis of the bright Seyfert galaxy IC 4329A. The Imaging X-ray Polarimetry Explorer (IXPE) observed the source for ~500 ks, supported by XMM-Newton (~60 ks) and NuSTAR (~80 ks) exposures. We detect polarisation in the 2-8 keV band with 2.97 sigma confidence. We report a polarisation degree of $3.3\pm1.1$ per cent and a polarisation angle of $78\pm10$ degrees (errors are 1 sigma confidence). The X-ray polarisation is consistent with being aligned with the radio jet, albeit partially due to large uncertainties on the radio position angle. We jointly fit the spectra from the three observatories to constrain the presence of a relativistic reflection component. From this, we obtain constraints on the inclination angle to the inner disc (< 39 degrees at 99 per cent confidence) and the disc inner radius (< 11 gravitational radii at 99 per cent confidence), although we note that modelling systematics in practice add to the quoted statistical error. Our spectro-polarimetric modelling indicates that the 2-8 keV polarisation is consistent with being dominated by emission directly observed from the X-ray corona, but the polarisation of the reflection component is completely unconstrained. Our constraints on viewer inclination and polarisation degree tentatively favour more asymmetric, possibly out-flowing, coronal geometries that produce more highly polarised emission, but the coronal geometry is unconstrained at the 3 sigma level., Comment: Accepted for publication in MNRAS, 13 pages, 9 figures

We present an X-ray spectro-polarimetric analysis of the bright Seyfert galaxy NGC4151. The source has been observed with the Imaging X-ray Polarimetry Explorer (IXPE) for 700 ks, complemented with simultaneous XMM-Newton (50 ks) and NuSTAR (100 ks) pointings. A polarization degree ${\Pi} = 4.9 {\pm} 1.1 \%$ and angle ${\Psi}= 86{\deg} {\pm} 7{\deg}$ east of north ($68\%$ confidence level) are measured in the 2-8 keV energy range. The spectro-polarimetric analysis shows that the polarization could be entirely due to reflection. Given the low reflection flux in the IXPE band, this requires however a reflection with a very large ($> 38 \%$) polarization degree. Assuming more reasonable values, a polarization degree of the hot corona ranging from ${\sim}4$ to ${\sim}8\%$ is found. The observed polarization degree excludes a spherical lamppost geometry for the corona, suggesting instead a slab-like geometry, possibly a wedge, as determined via Monte Carlo simulations. This is further confirmed by the X-ray polarization angle, which coincides with the direction of the extended radio emission in this source, supposed to match the disc axis. NGC4151 is the first AGN with an X-ray polarization measure for the corona, illustrating the capabilities of X-ray polarimetry and IXPE in unveiling its geometry., Comment: 9 pages, 4 figures

It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac Hamiltonian is invariant with respect to the rotation transformation, which indicates the dynamical (hidden) symmetry $ SU(2) $ of the Dirac equation. The total symmetry of the Dirac equation is the symmetry $ SO(3) \otimes SU(2) $. The generator of the $ SO(3) $ symmetry group is given by the total momentum operator, and the generator of $ SU(2) $ group is given by the rotation of the vector-states in the spinor space, determined by the Dirac, Johnson-Lippmann, and the new spinor invariants. It is shown that using algebraic approach to the Dirac problem allows one to calculate the eigenstates and eigenenergies of the relativistic hydrogen atom and reveals the fundamental role of the principal quantum number as an independent number, even though it is represented as the combination of other quantum numbers., Comment: 16 pages, no figures

Solutions of the Dirac equation for an electron in the Coulomb potential are obtained using operator invariants of the equation, namely the Dirac, Johnson-Lippmann and recently found new invariant. It is demonstrated that these operators are the spin invariants. The generalized invariant is constructed and the exact general solution of the Dirac equation are found. In particular, the explicit expressions of the bispinors corresponding to the three complete sets of the invariants, their eigenvalues and quantum numbers are calculated. It is shown that the general solution of one center Coulomb Dirac equation contains free parameters. Changing one or more of these parameters, one can transform one solution of the Dirac equation into any other. It is shown for the first time that these invariants determine electron spatial probability amplitude and spin polarization in each quantum state. Electron probability densities and spin polarizations are explicitly calculated in the general form for several electron states in the hydrogen-like energy spectrum. Spatial distributions of these characteristics are shown to depend essentially on the invariant set, demonstrating, in spite of the accidental degeneracy of energy levels, physical difference of the states corresponding to different spin invariants., Comment: 24 pages, 6 figures

The ideal Bose-gas with finite number $N$ of particles is investigated. The exact expressions for the partition functions and occupation numbers in the grand canonical, canonical and microcanonical ensembles are found. The asymp\-totic expressions (in the case $N\gg1$) for the partition functions and occupation numbers in the canonical and microcanonical ensembles are evaluated. It is shown that the chemical potential $\mu$ of the ideal Bose-gas can lie in the range $-\infty<\mu<\infty$ oppositely to the widely adopted opinion that the value of this potential is negative., Comment: 7 pages, no figures

The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and explicit expressions for the bispinors corresponding to the three sets of the invariants, their eigenvalues and quantum numbers are obtained. The general solution of the Dirac equation with the Coulomb potential is shown to contain free parameters, whose variation transforms one particular solution into any other and controls spatial electron probability amplitude and spin polarization. The electron probability densities and spin polarizations are obtained in the general form and calculated explicitly for some electron states in the hydrogen-like energy spectrum. The spatial distributions of these characteristics are shown to depend essentially on the invariant set, demonstrating physical difference of the states corresponding to different invariants., Comment: 24 pages, 6 figures

Square-octagon lattice underlies the description of a family of two-dimensional materials such as tetragraphene. In the present paper we show that the tight-binding model of square-octagon lattice contains both conventional and high-order van Hove points. In particular, the spectrum of the model contains flat lines along some directions composed of high-order saddle points. Their role is analyzed by calculating orbital susceptibility of electrons. We find that the presence of van Hove singularities of different kinds in the density of states leads to strong responses: paramagnetic for ordinary singularities and more complicated for high-order singularities. It is shown that the orbital susceptibility as a function of hoppings ratio $\alpha$ reveals the dia- to paramagnetic phase transition at $\alpha\approx 0.94$. This is due to the competition of paramagnetic contribution of high-order VHS and diamagnetic contribution of Dirac cones. The results for the tight-binding model are compared with low-energy effective pseudospin-1 model near the three band touching point., Comment: 13 pages, 5 figures

The description of the collective magnetorheological effect induced by magnetic field in magnetoactive elastomers is proposed. The condition of consistency is used between magnetic and mechanic momenta of forces exerted on magnetically uniaxial ferromagnetic particles in elastomer at their magnetization. The study shows that even in the case of small concentration of particles, the value of magnetically-induced shear can be anomalously large, reaching up to tens of percent. The deformation of magnetoactive elastomer can evolve critically, as a second-order phase transition, if magnetic field is aligned along the easy axis of particles., Comment: 9 pages, 3 figures

In frame of Dirac quantum field theory that describes electrons and positrons as elementary excitations of the spinor field, the generalized operator of the spin-orbit interaction is obtained using non-relativistic approximation in the Hamilton operator of the spinor field taking into account the presence of an external potential. This operator is shown to contain a new term in addition to the known ones. By an example of a model potential in the form of a quantum well, it is demonstrated that the Schroedinger equation with the generalized spin-orbit interaction operator describes all spin states obtained directly from the Dirac equation. The dependence of the spin-orbit interaction on the spin states in quasi-two-dimensional systems of electrons localized in a quantum well is analyzed. It is demonstrated that the electric current in the quantum well layer induces the spin polarization of charge carriers near the boundary surfaces of the layer, with the polarization of the charge carriers being opposite at the different surfaces. This phenomenon appears due to the spin-orbit interaction and is known as the spin Hall effect, which was observed experimentally in heterostructures with the corresponding geometry., Comment: 23 pages

An explanation is proposed for the recently observed in optical spectra of monolayer graphene giant increase in the Drude peak width under applied uniaxial strain. We argue that the underlying mechanism of this increase can be based on resonant scattering of carriers from inevitably present impurities such as adsorbed atoms that can be described by the Fano-Anderson model. We demonstrate that the often neglected scalar deformation potential plays the essential role in this process. The conditions necessary for the maximum effect of the giant Drude peak broadening are determined. It is stressed that the effect is strongly enhanced when the Fermi level gets closer to the Dirac point. Our theoretical analysis provides guidelines for functionalizing graphene samples in a way that would allow to modulate efficiently the Drude peak width by the applied strain., Comment: 16 pages, 7 figures; final version published in PRB

A theoretical analysis is presented on possible effects of disorder by dopants in high-temperature superconducting cuprate perovskites, to define their basic spectra of spin and electronic excitations, and the subsequent observable properties, especially doping dependence of superconducting order parameter. The central point in the proposed physical picture is formation of specific impurity subband within the insulating bandgap of initial undoped material, serving as a source for the system metallization and further transition into superconducting state with anisotropic order parameter., Comment: 20 pages, 11 figures

All relativistic corrections to the Scr{\"o}dinger equation which determine the interlink between spin and orbit of moving particles, are directly calculated from the Dirac equation using the spin invariant operators. It is shown that among the second order corrections there are not only the well-known Darwin and Thomas terms, but also the new ones. Only with the account of the latter corrections the energies found with the obtained spin-orbit interaction operator, coincide with the energies of the Dirac equation exact solution. The problem of electron spectrum in the quantum well type structures is studied in details and the physical reasons for the appearance of spin-orbit interaction operators in the Dresselhaus or Rashba form, are analyzed., Comment: 23 pages

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary transformation and shown to depend on the electron spin polarization. The general solution, being the only one, contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detailL: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov-Rashba coefficients are analytically obtained for both cases. The general solution allows - independently on the existence of the spin invariants - to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. In principle, this opens new possibilities of the spin degree of freedom control in spintronics via synthesis of heteroctructures of the desirable properties., Comment: 20 pages, 2 figures

Formation of localized impurity levels within the band gap in bigraphene under applied electric field is considered and the conditions for their collectivization at finite impurity concentration are established. It is shown that a qualitative restructuring of quasiparticle spectrum within the initial band gap and then specific metal-insulator phase transitions are possible for such disordered system and can be effectively controlled by variation of the electric field bias at given impurity perturbation potential and concentration. Since these effects can be expected at low impurity concentrations but at not too low temperatures, they can be promising for practical applications in nanoelectronics devices., Comment: 10 pages, 5 figures. Previous version was revised, some new discussion on observable effects of impurity band and a new figure were added

The problem of the spin states corresponding to the solutions of Dirac equation is studied. In particular, the three sets of the eigenfunctions of Dirac equation are obtained. In each set the wavefunction is at the same time the eigenfunction of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigenfunctions of Dirac equation describe three independent spin states. The energy spectrum is calculated for each of these sets for the case of quasi-two-dimensional electrons in a quantum well. It is shown that the standard Rashba spin-orbit interaction takes place in one of such states only. In another one this interaction is not formed at all, and for the third one it leads to the band spectrum which is anisotropic in the plane domain of the propagation of a free electron and is different from the isotropic spectrum of Rashba type.

The Bose-Einstein condensation (BEC) of magnons created by a strong pumping in ferromagnetic thin films of yttrium iron garnet used as systems of finite size is considered analytically. Such a peculiarity, typical for this magnetic material, as the presence of a minimum in the spectrum of spin waves at a finite value of the wave vector is taken into account. The definition of hightemperature BEC is introduced and its characteristics are discussed. A role of boundary conditions for spin variables is analyzed, and it is shown that in the case of free spins on the boundary the magnon lattice can form in the system. The factors responsible for its appearance are discussed., Comment: 21 pages, 4 figures

High fraction of the surface atoms considerably enhances the influence of size and shape on the magnetic and electronic properties of nanoparticles. Shape effects in ferromagnetic nanoparticles are well understood and allow to set and control the parameters of a sample that affect its magnetic anisotropy during production. In the present paper we study the shape effects in the other widely used magnetic materials -- antiferromagnets, -- which possess vanishingly small or zero macroscopic magnetization. We take into account the difference between the surface and bulk magnetic anisotropy of a nanoparticle and show that the effective magnetic anisotropy depends on the particle shape and crystallographic orientation of its faces. Corresponding shape-induced contribution to the magnetic anisotropy energy is proportional to the particle volume, depends on magnetostriction, and can cause formation of equilibrium domain structure. Crystallographic orientation of the nanoparticle surface determines the type of domain structure. The proposed model allows to predict the magnetic properties of antiferromagnetic nanoparticles depending on their shape and treatment., Comment: 15 pages, 6 figures, to be submitted to Journal of Physics Condensed Matter

We calculate the transmission coefficient for electrons passing through the helically shaped potential barrier, which can be, for example, produced by DNA molecules., Comment: 4 pages; typos corrected

Macroscopic properties of multiferroics, the systems that show simultaneously two types of ordering, could be controlled by the external fields of different nature. We analyze the behavior of multiferroics with antiferro-(AFM) and ferromagnetic (FM) ordering under the action of external magnetic and stress fields. A combination of these two fields makes it possible to achieve macroscopic states with different domain structures. The two-domain state obtained in this way shows a linear dependence of macroscopic strain vs magnetic field which is unusual for AFMs. A small but nonzero stress applied to the sample can also result in the bias of the magnetization vs magnetic field dependence., Comment: Published in UJPh (http://www.ujp.bitp.kiev.ua)

We study the electronic properties of 2D electron gas (2DEG) with quadratic dispersion and with relativistic dispersion as in graphene in the inhomogeneous magnetic field consisting of the Aharonov-Bohm flux and a constant background field. The total and local density of states (LDOS) are obtained on the base of the analytic solutions of the Schr\"{o}dinger and Dirac equations in the inhomogeneous magnetic field. It is shown that as it was in the situation with a pure Aharonov-Bohm flux, in the case of graphene there is an excess of LDOS near the vortex, while in 2DEG the LDOS is depleted. This results in excess of the induced by the vortex DOS in graphene and in its depletion in 2DEG., Comment: 20 pages, 7 figures; final version published in PRB

Effects of impurities and disorder on quasiparticle spectrum in superconducting iron pnictides are considered. Possibility for occurrence of localized energy levels due to impurities within the superconducting gap and the related modification of band structure and of superconducting order parameter are discussed. The evolution of superconducting state with impurity doping is traced., Comment: 9 pages, 8 figures

We analyze a possible superconductivity in the hole-doped system of layered hydrogenized graphene by taking into account thermal fluctuations of the order parameter. In particular, we demonstrate that in the one-layer case the values of the high mean-field (MF) critical temperature $T_{c}^{MF}\sim 80-90K$, predicted recently by Savini et al \cite{Savini}, do not alter significantly due to the fluctuations, and the Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the vortex superconductivity is almost the same as the MF temperature at doping 0.01-0.1. We show that in the case of multilayer system, when the coupling between the layers stabilizes the superconducting phase in the form of fluxon superconductivity, the critical temperature $T_{c}$ can increase dramatically to the values $\sim 150K$, higher than the corresponding values in cuprates under ambient pressure.

The theoretical approach proposed recently for description of redistribution of electronic charge in multilayered selectively doped systems is modified for a system with finite number of layers. A special attention is payed to the case of a finite heterostructure made of copper-oxide layers which are all non-superconducting (including non-conducting) because of doping levels being beyond the well-known characteristic interval for superconductivity. Specific finite structures and doping configurations are proposed to obtain atomically thin superconducting heterojunctions of different compositions., Comment: 4 pages, 3 figures, two bibliography references were updated

Solid oxygen is a unique molecular crystal whose phase diagram is mostly imposed by magnetic ordering, i.e., each crystal phase has a specific magnetic structure. However, recent experiments showed that high-pressure $\delta$-phase is implemented in different magnetic structures. In the present paper we study the role of interplane exchange interactions in formation of the magnetic structures with different stacking sequences of the close-packed planes. We show that temperature-induced variation of intermolecular distances can give rise to compensation of the exchange coupling between the nearest close-packed planes and result in the phase transition between different magnetic structures within $\delta$-O$_2$. Variation of the magnetic ordering is, in turn, accompanied by the step-wise variation of interplane distance governed by space and angular dependence of interplane exchange constants., Comment: 16 pages, 6 figures

We find the distribution of the electromagnetic field inside and outside a dielectric disk resonator placed in He-II. It is shown that this field consists of a collection of "circular" (c-) photons. The wave function \Psi_c of a c-phonon for the He-II + disk system is calculated in the zero-order approximation in interaction. Due to the symmetry of the problem, the structure of \Psi_c is such that a c-phonon possesses, similarly to a c-photon of the resonator, a definite energy and an angular momentum with respect to the disk axis, but it does not possess a definite momentum in the disk plane., Comment: 9 pages, 1 figure

We carry out a comparative study of electronic properties of 2D electron gas (2DEG) in a magnetic field of an infinitesimally thin solenoid with relativistic dispersion as in graphene and quadratic dispersion as in semiconducting heterostructures. The problem of ambiguity of the zero mode solutions of the Dirac equation is treated by considering of a finite radius flux tube which allows to select unique solutions associated with each $\mathbf{K}$ point of graphene's Brillouin zone. Then this radius is allowed to go to zero. On the base of the obtained in this case analytical solutions in the Aharonov-Bohm potential the local and total density of states (DOS) are calculated. It is shown that in the case of graphene there is an excess of LDOS near the vortex, while in 2DEG the LDOS is depleted. This results in excess of the induced by the vortex DOS in graphene and in its depletion in 2DEG. We discuss the application of the results for the local density of states for the scanning tunneling spectroscopy done on graphene., Comment: 15 pages, 4 figures; final version published in PRB

An asymptotic expansions for the grand partition function of ideal Bose gas in the canonical ensemble with arbitrary number of particles is obtained. It is shown that the expressions found are valid in the whole temperature region, the critical temperature included. A comparison between the asymptotic formulas for Bose-condensate fluctuations and the exact ones is carried out and their quantitative agreement is established.

By means of numerical simulation we confirm that in graphene with point defects a quasigap opens in the vicinity of the resonance state with increasing impurity concentration. We prove that states inside this quasigap cannot longer be described by a wavevector and are strongly localized. We visualize states corresponding to the density of states maxima within the quasigap and show that they are yielded by impurity pair clusters.

An attempt is made to consider the difference between the proccesses of the Bose-Einstein condensation of particles and quasiparticles. An equation for particle number of the Bose-condensate as a function of the total number of particles in the system is obtained. This equation is also written for the caseof quasiparticles with taking into account their creation by pumping and the existence ofequilibriumthermal excitations in the system. From the analysis of both these equations the chemical potential of pumped quasiparticles and their number in the condensate as a function of pumping intensity is found. It is shown that for low energy quasiparticles the proccess of Bose-condensation begins and proceeds at arbitrary temperatures high enough included., Comment: 10 pages

A simple theoretical model is proposed to describe the recent experimental results on formation of induced superconducting state and anomalous tunneling characteristics in selectively doped multilayered nanostructures based on La$_2$CuO$_4$ perovskite. In particular, it is shown that the structure composed from the nominally non-superconducting (undoped and overdoped) layers turns to be superconducting with superconductivity confined to narrow regions near the interfaces, in agreement with the experimental observations., Comment: 4 pages, 4 figures, revtex

An attempt is made to explain the nature of the electric signal observed in He II in a second-sound standing wave. Using the general quantum-mechanical principles, we show that, due to interatomic interaction, each atom of He-II acquires a small fluctuating induced dipole moment. A directed flux of microscopic vortex rings -- which, together with phonons, are thermal excitations of He II -- forms in the second-sound standing halfwave. This flux partially orders the chaotically oriented dipole moments of the atoms, which results in volume polarization of He II. The observed electric induction can be explained theoretically under the assumption that each vortex ring possesses a dipole moment of the order of ten atomic moments. It is shown also that the theoretical value of the voltage U induced in He II by the volume system of dipoles strongly depends on the dimensions of the resonator for dipoles of any origin. The experimental value of U is the same for two resonators of different size; therefore, this voltage may be not connected with the volume polarization of He II., Comment: 3 pages

We analyze the spectral properties of a phenomenological model for a weakly doped two-dimensional antiferromagnet, in which the carriers move within one of the two sublattices where they were introduced. Such a constraint results in the free carrier spectra with the maxima at ${\bf k}=(\pm \pi /2 ,\pm \pi /2)$ observed in some cuprates. We consider the spectral properties of the model by taking into account fluctuations of the spins in the antiferromagnetic background. We show that such fluctuations lead to a non-pole-like structure of the single-hole Green's function and these fluctuations can be responsible for some anomalous "strange metal" properties of underdoped cuprates in the nonsuperconducting regime., Comment: Submitted to Condensed Matter Physics

In the framework of phenomenological model we consider dynamics of a compensated collinear antiferromagnet (AFM) in the presence of spin-polarised current. The model is based on the assumption that AFM spins are localised and spin torque is transferred to each magnetic sublattice independently. It is shown that in AFM spin current i) can be a source of the "negative friction"; and ii) modifies spin-wave frequencies. Equilibrium state of AFM can be destabilized by the current polarized in parallel to AFM vector. Threshold current at which the loss of stability takes place depends upon the magnetic anisotropy of AFM., Comment: 9 pages, 3 figures, submitted to J. Mag. Soc. Japan

The theoretical description of quantum phase transition, induced by the external magnetic field, into antiferromagnetic state in the van Vleck - singlet - magnet with a single-ion anisotropy of "easy-plane" type and ion spin S=1 is proposed. It is shown that the spin polarization of the ground non-degenerated state proves to be the order parameter of such a transition and that the Landau thermodynamic approach can be employed for its (transition) description. The magnetic properties which include the field behavior of the magnetization and magnetic susceptibility of the antiferromagnetic phase in the fields of different directions are studied. The peculiarities of induced magnetostriction in van Vleck antiferromagnet, which as well as magnetization has a singularity in the phase transition point, are investigated. An attempt is made for qualitative comparison of results obtained with avaliable experimental data., Comment: 21 pages, 6 figures

In the present paper we generalised a phenomenological model developed in \cite{gomo:2005} for the description of magnetostructural phase transitions and related peculiarities of elastic properties in solid oxygen under high pressure and/or low (below 40 K) temperature. We show that variation of all the lattice parameters in the vicinity of $\alpha\beta$-phase transition is due to both the shift of basal closed packed planes and appearance of the long-range magnetic order. Competition between these two factors from one side and lattice compression below $T_{\alpha\beta}$ from another produces non monotonic temperature dependence of lattice parameter $b$ (along monoclinic axis). Steep decrease of the sound velocities in the vicinity of $T_{\alpha\beta}$ can be explained by the softening of the lattice with respect to shift of the close-packed planes (described by the constant $K_2$) prior to phase transition point. We anticipate an analogous softening of sound velocities in the vicinity of $\alpha \delta$-phase transition and non monotonic pressure dependence of sound velocities in $\alpha$-phase., Comment: 11 pages, 8 figures, to appear in Low Temperature Physics, v.33, N6, 2007, materails presented at the Conference CC-2006, Kharkov, 2006

Bose condensation of quasiparticles in physical systems of finite size iz considered for the case of ferromagnetic thin films. It is shown that in accordance with present-day experimental capabilities which permit one to achieve densities of long-wave spin excitation of 1018-1019 cm-3, in such films the formation of condensate of such quasiparticles begins at temperatures T~100 K (room one including). It is found that Bose condensation is accompanied by scaling phenomenon according to which the main thermodynamic variable is not the number N of particles but the ratio N/T. This indicates that condensation of magnons can be observed at relatively low magnon densities. The roles played by the shape of the spectrum and film thickness are analyzed., Comment: 28 pages, 10 figures

The superconducting properties of a recently proposed phenomenological model for a weakly doped antiferromagnet are analyzed, taking into account fluctuations of the phase of the order parameter. In this model, we assume that the doped charge carriers can't move out of the antiferromagnetic sublattice they were introduced. This case corresponds to the free carrier spectra with the maximum at ${\bf k}=(\pm \pi /2 ,\pm \pi /2)$, as it was observed in ARPES experiments in some of the cuprates in the insulating state [1]. The doping dependence of the superconducting gap and the temperature-carrier density phase diagram of the model are studied in the case of the $d_{x^{2}-y^{2}}$ pairing symmetry and different values of the effective coupling. A possible relevance of the results to the experiments on high-temperature superconductors is discussed., Comment: 16 pages, 4 figures

The long disputed issue of the limiting value of quasiparticle density of states $\r(0) = \r (\e \to 0)$ in a \emph{d-}wave superconductor with impurities (\emph{vs} its linear vanishing, $\r_0(\e) \propto |\e|/\D$, near the nodal point $\e = 0$ in a pure system with the gap parameter $\D$) is discussed. Using the technique of group expansions of Green functions in complexes of interacting impurities, it is shown that finite $\r(0)$ value is possible if the (finite) impurity perturbation $V$ is spin-dependent (magnetic). The found value has a power law dependence on the impurity concentration $c$: $\r(0) \propto \r_N c^{n}$, where $\r_N$ is the normal metal density of states and $n \geq 2$ is the least number of impurities in a complex that can localize nodal quasiparticle. This result essentially differs from the known predictions of self-consistent approximation: $\r(0) \propto \r_N \sqrt {c/\r_N\D}$ (for the unitary limit $V \to \infty$) or $\r(0) \propto (\D/cV^2)\exp(-\D/cV^2\r_N)$ (for the Born limit $|V|\r_N \ll 1$). We predict also existence of a narrow interval (mobility gap) around the Fermi energy, where all the states are localized on proper impurity clusters, leading to exponential suppression of low-temperature kinetics., Comment: 6 pages, 5 figures, revtex, some new references were added and the used approximations were explained

It is demonstrated that in a two--band 2D system the resonance state is manifested close to the energy of the Dirac point in the electron spectrum for the sufficiently large impurity perturbation. With increasing the impurity concentration, the electron spectrum undergoes the rearrangement, which is characterized by the opening of the broad quasi--gap in the vicinity of the nodal point. If the critical concentration for the spectrum rearrangement is not reached, the domain of localized states remains exponentially small compared to the bandwidth., Comment: 4 pages, 1 figure