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The superconducting properties of the one-dimensional model of “relativistic” fermions with attraction generated by antiferromagnetic (Heisenberg) pair superexchange spin interaction are studied. Namely, we demonstrate that such a pairing in this system takes place in the nematic channel, with extended s-wave symmetry, where the attraction between fermions mostly takes place when the fermions occupy the nearest sites. It is demonstrated, that the zero-temperature properties of such a system are rather different from the “standard” case of superconductivity with local attraction. For instance, the order parameter has an unusual helical momentum dependence, [Formula: see text], where a is the lattice parameter and the dependence of the gap on doping has a bell shape, qualitatively similar to cuprate high- Tc superconductors. Finally, the smooth transition from the overlapping pair to the local pair regime (or BCS–BEC crossover) in the nematic phase takes place at much lower values of doping as compared to the local pairing case, i.e., the “relativistic 1D” nematic superconductor is much less “friendly” to the local pairs. We also discuss the possible relation of the properties of this model to the superconducting properties of twisted graphene.

We analyze static and nonequilibrium superconducting properties of a 2D relativistic-like model system with local electron-electron interaction, Rashba spin-orbit interaction α R in presence of time-dependent in-plane magnetic field H( t). It is shown that similar to the 2D case with ordinary massive quasiparticle dispersion [Formula: see text] at large fields, such a system demonstrates a nonhomogeneous superconducting stripe phase with the order parameter [Formula: see text] (B is the magnetic induction, υF is the Fermi velocity, n is the normal to the plane, μ B is the Bohr magneton, and [Formula: see text]) where the stripes are oriented along the B direction. In the considered system, the inter-stripe period L and the magnitude of the magnetic field B are related by a universal relation [Formula: see text]. Contrary to the case of massive quasiparticles, where the condition [Formula: see text] can be, in principle, satisfied by increasing α R or by charge doping (Fermi velocity decreasing), in a relativistic-like system, where υF is doping-independent and one-two orders of magnitude larger than typical Fermi velocity in the “standard” 2D systems, the stripe phase can be the ground state at a rather low doping level. We also analyzed the nonequilibrium properties of the system with a focus on the melting of the stripe order (when the magnetic field is quenched to a lower value) and stripe dynamics (when the field is rotated by 90° degrees) and found several notable results. In particular, it was shown that the stripe domains melt according to law [Formula: see text] at initial times, while at longer times they shrink exponentially. In the case of the flipped magnetic field, the stripe orientation gradually turns from x- to y-direction, and the intermediate “crossed-stripe” phase takes place during times of order of picoseconds. Such a crossed phase is built of periodic superconducting bubbles that potentially may have applications in modern ultrafast superconducting technologies.

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., 16 pages, no figures

We consider the finite ribbons of graphene with two principal orientations, zigzag and armchair, of their edges to study in detail impurity effects on their edge states. An alternative to the known description of quasiparticle states in terms of transversal standing waves is proposed in the recurrence relations for their spectra vs discrete numbers of atomic chains in the ribbon, permitting to simplify the Green function approach to the disorder effects in these systems. The derived analysis shows the microscopic mechanisms of perturbation by different types of impurities on low energy states and clarifies how the stability of topological states in zigzag systems to disorder is related to the discrete amplitudes of these states across the ribbon. An opposite possibility for Mott localization under local impurity perturbations is found for armchair type nanoribbons but at special values of their width.

The paper is devoted to the theory of an ideal Bose-gas with a finite number N of particles. The exact expressions for the partition functions and occupation numbers of the model in the grand canonical, canonical, and microcanonical ensembles are found. From the calculations, it is followed that, oppositely to the accepted opinion that the chemical potential μ of an ideal Bose-gas is only negative, it can take values in the range −∞ < μ < ∞. The asymptotic expressions (in the case N ≫ 1) for the partition functions and occupation numbers for all above-mentioned thermodynamic ensembles are also evaluated., Стаття присвячена теорiї iдеального бозе-газу зi скiнченною кiлькiстю N частинок. Знайдено точнi вирази для функцiй розподiлу та чисел заповнення для даної моделi у великому канонiчному, канонiчному та мiкроканонiчному ансамблях. З розрахункiв випливає, що на вiдмiну вiд загальноприйнятої думки, що хiмiчний потенцiал μ iдеального бозе-газу лише негативний, вiн може приймати значення в дiапазонi −∞ < μ < ∞. Також оцiнено асимптотичнi вирази (у випадку N ≫ 1) для функцiй розподiлу i чисел заповнення для всiх вищезгаданих термодинамiчних ансамблiв.

A novel family of disordered systems is proposed. This family belongs to the class of systems containing random substitutional non-Hermitian impurities. We limit our consideration to a rather simple case when the presence of substitutional point defects results in the model Hamiltonian featuring a diagonal disorder. In contrast to known models of non-Hermitian impurities, the nonzero density of states for each isolated from the host impurity is restricted to a continuous band of finite width. A method to construct corresponding impurity Hamiltonians is provided.

The electronic spectrum of graphene with a single point impurity is considered. Local densities of states at the impurity site and its nearest neighbors are calculated analytically. Their evolution...

This review is an attempt to consistently examine the electronic spectrum of graphene containing defects (such as adsorbed atoms, substitutional atoms, vacancies) that can be adequately described using the Lifshitz model. Therefore, the known Hamiltonian of this model is chosen for the case of two-dimensional relativistic electrons, and the criteria for the appearance of an impurity resonance near the Dirac point are provided. The theory of concentration band structure transformation in graphene is outlined, from which it follows that a transport gap opens in the vicinity of the impurity resonance energy when a specific value of the impurity concentration is reached. Along the way, the question of whether or not it is possible (or impossible) for Dirac quasiparticles to become localized in such a spatially disordered system is analyzed. Based on this, it is feasible to explain and describe the recently observed in impure graphene phenomenon of metal-insulator transition, which turns out to be a direct consequence of the system’s Fermi energy falling into the domain of the transport gap. The concept of local spectrum rearrangement, which can also unfold as the defect concentration increases, is introduced and justified for graphene. We formulate the physical reasons why the minimum of graphene’s low-temperature conductivity dependence on the Fermi energy of electrons does correspond to the impurity resonance energy, and not the Dirac point, as it has been claimed in a number of theoretical and experimental studies. Furthermore, the mentioned minimum value proves to be not universal, but is dependent, instead, on the concentration of defects. The analytical considerations of the impurity effects are accompanied by numerical simulations of the examined system, and a complete correspondence between these two approaches is established as a result. In particular, the general scenarios of spectrum rearrangement, electron state localization, as well as of effects having a local nature, are confirmed.This review is an attempt to consistently examine the electronic spectrum of graphene containing defects (such as adsorbed atoms, substitutional atoms, vacancies) that can be adequately described using the Lifshitz model. Therefore, the known Hamiltonian of this model is chosen for the case of two-dimensional relativistic electrons, and the criteria for the appearance of an impurity resonance near the Dirac point are provided. The theory of concentration band structure transformation in graphene is outlined, from which it follows that a transport gap opens in the vicinity of the impurity resonance energy when a specific value of the impurity concentration is reached. Along the way, the question of whether or not it is possible (or impossible) for Dirac quasiparticles to become localized in such a spatially disordered system is analyzed. Based on this, it is feasible to explain and describe the recently observed in impure graphene phenomenon of metal-insulator transition, which turns out to be a direct con...

Ideal Bose-gas with finite particle number N is investigated. It is shown that the well-known Bose–Einstein distribution of particles over their quantum states consists of two terms — Bose–Einstein term and an additional N-dependent one. The statement that the chemical potential of the ideal Bose-gas should be negative requires to be also corrected. It is obtained that the analytically calculated observables rather slowly approach the thermodynamic limit following the law N−1/3lnN.

This article attempts a point-by-point review of the electron spectrum of graphene containing defects (adsorbed atoms, substitutional atoms, vacancies) that can be adequately described within the Lifshitz model. In this regard, the known Hamiltonian for this model is calculated for the case of two-dimensional relativistic electrons, and the criteria for occurrence of an impurity resonance near a Dirac point are given. The theory of concentration band structure transformation of graphene is presented, from which it follows that a transport gap is opened upon reaching a strictly defined value of impurity concentration in the neighborhood of the energy of impurity resonance. At the same time, the question of the possibility (or impossibility) of localization in such a {spatially disordered system} of Dirac quasiparticles is analyzed. Based on this, it is possible to provide an explanation and present a description of a phenomenon recently observed in {impure graphene}, the metal-dielectric transition that appears as a direct consequence of the decrease of the Fermi energy of the system in the region of a transport gap. The concept of local spectrum rearrangement of graphene, which also occurs during the process of increased concentration of defects in it, is introduced and substantiated. Physical reasons are formulated, by which the position of the minimum of the low-temperature conductivity of graphene as a function of the Fermi energy of electrons corresponds to the impurity resonance energy rather than to the Dirac point, as has been validated in a number of theoretical and test studies. Here, it appears that the minimum value is not a universal magnitude, but depends on the concentration of defects. Analytical examination of impurity effects is accompanied by numerical modeling of the system under study, as a result of which complete correspondence has been established between these two approaches. In particular, the overall picture of spectrum rearrangement, localization of electron states, and also the effects having local nature are confirmed.

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) orderingunder 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., Макроскопічними властивостями мультифероїків, тобто речовин, в яких співіснують два типи впорядкування, можна керувати за допомогою полів різної природи. В даній роботі проана ізовано поведінку мультифероїків з антиферо- (АФМ) та феромагнітним (ФМ) впорядкуванням під дією зовнішнього магнітного поля та механічного напруження. Комбінація цих двох полів дозволяє отримати макроскопічні стани з різною доменною структурою. Отриманий таким способом дводоменний стан демонструє нетипову для АФМ лінійну залежність макроскопічної деформації від зовнішнього магнітного поля. Мале, але ненульове механічне напруження приводить також до зсуву кривої залежності макроскопічної намагнічуваності від магнітного поля (ефективному "підмагнічуванню").

The dependence of the position of the mobility edge on the impurity concentration during the transformation of the electronic band structure is considered in a disordered system described by the Lifshitz model. Concentration dependence of the mobility threshold caused by variation of the threshold parameter in the Ioffe–Regel criterion is analyzed. It is demonstrated that the critical concentration of the impurity, which triggers the transformation of the band structure, changes slightly with variation of this parameter, while the corresponding position of the mobility edge at this concentration remains stable. The prerequisites for the existence of such concentration intervals, within which the mobility edge is shifted in proportion to the cubic root of the impurity concentration, are discussed.

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

We describe a first-order phase transition in an isotropic non-Heisenberg ferromagnet induced by a magnetic field with a fourth-order spin exchange interaction at temperatures above the Curie point. The field behavior of the magnetization is analyzed and the temperature dependences of the critical fields of the stability of the paramagnetic and ferromagnetic phases as well as the critical field of the phase transition between them are determined. It is shown that this first-order phase transition has a finite amplitude of the magnetization jump and can occur in small magnetic fields. An H–T phase diagram is presented. It is found that the amplitude of the phase jump during the magnetic field-induced transition from the paramagnetic to the ferromagnetic phase can exceed the magnitude of the entropy change of an isotropic Heisenberg ferromagnet by two orders of magnitude when it is magnetized at the Curie point. It is shown that the expansion of the free energy model up to the 6th power in magnetization can only qualitatively describe the entropy behavior in the phase transition between the paramagnetic and ferromagnetic phases.

A survey is done on the effects of impurities in different types of superconductors, both conventional and unconventional, on their electronic spectra and physical properties. These effects can be generally divided on the base of validity (or not) for them of the known Anderson theorem, which is determined by the symmetries of the superconducting state vs those of the impurity perturbation. In this regard, the unconventional behavior can be naturally attributed to this theorem's failure when the impurity effects are generally much stronger and more diverse. Specific forms of such perturbations in different superconducting systems are analyzed and they reveal a variety of possible scenarios for quasiparticle spectra modification, including formation of several superconducting phases, distinguished by the types of specific narrow bands within the main spectrum gap. These phases and transitions between them, including the transition to the normal metal state, present a lot of unconventional features that can...

We present a theoretical description of a quantum phase transition in a dimerized antiferromagnet, induced by an external magnetic field. The description of such transitions is constructed by determining the minimum of the Lagrange function which depends on the parameters of the ground-state crystal wavefunction. We determine that during a crystal transition from the singlet state of the dimer to the state with a noncollinear spin orientation, an order-order type phase transition occurs. We show that in the case of a single-axis character of the exchange anisotropy, the location of the quantum phase transition critical point is affected by the spin-spin interactions inside the dimer. Additionally, analogous to the classical Neele antiferromagnets, single-axis type anisotropic spin-spin interactions between dimers, shift the point of the spin-flip transition from the noncollinear antiferromagnetic phase to the ferromagnetic phase.

The problem of the electron spectrum in a quasi-two-dimensional space (such as interfaces, heterostructures, and surfaces) is set up and analytically solved based on the fundamental Dirac equation. It is demonstrated that using the unitary transformation method and the method of spin invariants to solve the Dirac equation leads to identical results. The eigen bispinors of the Dirac equation are found, and the way in which their diversity arises due to the arbitrariness of the spin-quantization axis direction is demonstrated. The features of electron behavior in a parabolic quantum well are considered.

On the basis of the tight-binding method, the Green's function for a material with honeycomb crystal lattice containing a vacancy was studied. Well-known and commonly used models for description of a single vacancy were considered, and their equivalence was analytically demonstrated. It was also shown that the contributions to the density of quasiparticle states from both sublattices of the honeycomb lattice are identical, except for zero energy, irrespective of which sublattice contains the vacancy.

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., 20 pages, 2 figures

The magnetization of a two-sublattice Ising antiferromagnet with easy-plane single-ion anisotropy, which is accompanied by two phase transitions, has been studied. The both phase transitions are induced by the magnetic field. One of them is isostructural, i.e., the system symmetry remains unchanged and a transition between two antiferromagnetic states with different sublattice magnetizations takes place. The other phase transition occurs when the antiferromagnetic state transforms into the ferromagnetic one. At both phase transitions, the field dependence of the system entropy has two successive positive jumps, which is not typical of ordinary antiferromagnets. On the other hand, if the temperature of the system is higher than the tricritical temperature of the isostructural phase transition, there appears a continuous maximum in the field dependence of the entropy.

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function 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 eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.

Antiferromagnets (AFM) with a zero, or very small macroscopic magnetization, are promising materials in spintronics. Based on generalized Landau-Lifshitz equations, we examine the magnetic dynamics of three-sublattice AFM in the presence of a spin-polarized current, and in particular, the switching processes between different equilibrium states. We found the conditions for effective switching by pulsed and DC, as well as by an external magnetic field. We examined the features of stationary dynamic states, caused by the current. The obtained results can be used to develop high-speed elements of AFM-based memory materials.

It is shown that the first-order isostructural magnetic phase transition between antiferromagnetic phases with different magnitudes of the antiferromagnetism vector induced by an external magnetic field in Ising antiferromagnets can be related to entropy. It is found that, depending on the temperature, the entropy jump and the corresponding heat release can change their signs at the phase transition point. In the low-temperature region of the metamagnetic first-order phase transition the entropy jump is positive, while the entropy jump is negative near the triple point for isostructural magnetic phase transitions.

We present an overview of our recent results on quantum magnetic oscillations in new functional materials. We begin with the Lifshitz and Kosevich approach for quasi-2D layered materials and obtain general formulas for the oscillatory parts of the grand thermodynamic potential and magnetization. Then we consider the oscillations of the Nernst–Ettingshausen coefficient which consists of thermal and magnetization parts. The difference between normal and Dirac carriers is also discussed. To conclude we consider a model for multilayer grapheme which allows to calculate exactly the Berry phase which remains undetermined in the Lifshitz–Kosevich approach. The magnetic oscillations of the density of states and capacitance for different number of the carbon layers are described.

Spintronics of antiferromagnets is a new and rapidly developing field of the physics of magnetism. Even without macroscopic magnetization, antiferromagnets, similar to ferromagnetic materials are affected by spin-polarized current, and as in ferromagnets this phenomenon is based on a spin-dependent interaction between localized and free electrons. However, due to the nature of antiferromagnetic materials (complex magnetic structure, essential role of exchange interactions, absence of macroscopic magnetization) the study of possible spintronic effects requires new theoretical and experimental approaches. The purpose of this review is to systemize and describe recent developments in this area. After presenting the main features of structure and behavior of antiferromagnets various microscopic and phenomenological models for description of the current-induced phenomena in heterostructures containing ferro- and antiferromagnetic layers are considered. The questions related to an effect of antiferromagnetic ordering on an electric current, as well as the questions of possible creation of fully antiferromagnetic spin valves are discussed. In addition, we briefly discuss available experimental results and try to interpret them.

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 Schr¨odinger 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., В рамках квантової теорiї поля Дiрака, що описує електрони i позитрони як елементарнi збудження спiнорного поля, переходом до нерелятивiстського наближення в операторi Гамiльтона спiнорного поля з урахуванням наявностi зовнiшнього потенцiалу знайдено узагальнений оператор спiн-орбiтальної взаємодiї. Показано, що цей оператор мiстить окрiм вiдомих доданкiв також новий внесок. На прикладi модельного потенцiалу у виглядi квантової ями показано, що рiвняння Шредiнгера з таким узагальненим оператором спiн-орбiтальної взаємодiї описує всi спiновi стани, одержанi з самого рiвняння Дiрака. Дослiджено залежнiсть спiн-орбiтальної взаємодiї вiд спiнового стану у квазiдвовимiрних локалiзованих в площинi квантової ями електронних системах. Показано, що електричний струм у шарi квантової ями iндукує спiнову поляризацiю носiїв поблизу граничних поверхонь шару з протилежною поляризацiєю на протилежних поверхнях, що цiлком зумовлено дiєю узагальненої спiн-орбiтальної взаємодiї i вiдомо як спiновий ефект Холла, що i спостерiгалося експериментально у структурах з подiбною геометрiєю.

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 high-temperature 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

A Green function analysis is developed for the quasiparticle spectrum of 2D graphene sheets with different types of substitutional disorder, including vacancies. Impurity effects in this system are found to be anomalous, are compared to those in well-known doped semiconductors, and are explained in terms of conical singularities in the band spectrum of pure graphene. Criteria for the appearance of localized states on clusters of impurity scatterers and for qualitative restructuring of the band spectrum are established and the possibility of a distinctive metal/insulator transition when vacancies are present is discussed.

We study two-dimensional electronic gas (2DEG) in the background of the Aharonov–Bohm and constant magnetic fields. The problem of ambiguity of the solutions of the Schrodinger equation is investigated by introducing a finite radius of the flux tube, which then set to zero. Wave functions and spectrum of the 2DEG Hamiltonian are used to construct an expression for the local density of states (LDOS). We obtain that LDOS has a depletion near the origin of the vortex and new peaks, which can’t be explained by using Landau levels theory.

The revision is made of Green function methods that describe the dynamics of electronic quasiparticles in disordered superconducting systems with d-wave symmetry of order parameter. Various types of impurity perturbations are analyzed within the simplest T-matrix approximation. The extension of the common self-consistent T-matrix approximation (SCTMA) to the so-called group expansions in clusters of interacting impurity centers is discussed and hence the validity criteria for SCTMA are established. A special attention is paid to the formation of impurity resonance states and localized states near the characteristic points of energy spectrum, corresponding to nodal points on the Fermi surface.

In this paper, we study the superconducting properties of a two-dimensional model with an additional (insulating) gap Δins, which depends on temperature and doping. In particular, we study the doping evolution of the Berezinskii–Kosterlitz–Thouless critical temperature Tc and the superconducting pseudogap temperature TMFc at different values of Δins by taking into account the hydrodynamic fluctuations of the superconducting order parameter. We demonstrate that the presence of the gap Δins affect the values of the superconducting gap and temperatures Tc and TMFc in the region of the carrier densities where the gap Δins approaches to zero. In particular, the derivatives of these quantities have a jump in this region. We discuss possible relevance of the results to high-temperature superconductors.

The quantum phase transition induced by an external magnetic field in a dimerized spin crystal from its singlet ground state to an antiferromagnetic ordered state is examined under the assumption that the exchange interaction is antiferromagnetic, both within dimers and between them. It is shown that during this transition the magnetic polarization of the ions within a dimer and, therefore, of the dimers as a whole, is critical. The orientations and projections of the spin vectors in the magnetically ordered phase depend on the applied magnetic field, while the magnetic susceptibility of this essentially quantum phase remains (similarly to the case of a classical Neel antiferromagnet) constant as the spins of the magnetic sublattices undergo reorientation.

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.

We study the superconducting properties of a doped one-layer graphene by using a model in which the interparticle attraction is caused by a boson (phonon-like) excitations. We study the dependence of the superconducting gap Δ and the mean-field critical temperature TcMF on the carrier density, attraction strength, and characteristic (Debye) bosonic frequency. In addition, we study the temperature-carrier density phase diagram of the model by taking into account the thermal fluctuations of the order parameter. We show that the fluctuations result in a significant suppression of TcMF, such that the real (Berezinskii-Kosterlitz-Thouless) critical temperature Tc is much lower than TcMF. The region Tc

An attempt is made to determine the difference between Bose–Einstein condensation of particles and quasiparticles. An equation is obtained for the number of particles in a Bose–Einstein condensate as a function of the total number of particles in the system. This equation is also written for quasiparticles taking account of their creation by external pumping and the presence of equilibrium thermal excitations in the system. Analyzing both equations, the chemical potential of the pumped quasiparticles and their number in the condensate are found as a function of the pumping intensity. A condition under which the Bose–Einstein condensation of low-energy quasiparticle excitations starts and occurs at any, including quite high, temperatures is found.

The spectral function of graphene with point substitutional defects is calculated for different impurity concentrations. It is demonstrated that features in the spectral function of graphene observed in ARPES experiments can be caused by the presence of a well-defined resonance state and are clearly pronounced at the impurity concentrations, which are of the order of the critical concentration for the impurity-induced spectrum rearrangement.