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V. M. Loktev

Publications and source records attributed to V. M. Loktev.

At least 19 recordsLinked to original sources
arXiv2024

Topological conditions for impurity effects in graphene nanosystems

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.

cond-mat.mes-hall↗
arXiv2024

Input of the Coulomb law modification to the Lamb shift of the hydrogen atom

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.

quant-ph↗
arXiv2022

Algebra of the spinor invariants and the relativistic hydrogen atom

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.

quant-ph↗
arXiv2021

General solution vs spin invariant eigenstates of the Dirac equation with the Coulomb potential

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.

cond-mat.mes-hall↗
arXiv2021

Orbital susceptibility of T-graphene: Interplay of high-order van Hove singularities and Dirac cones

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 $α$ reveals the dia- to paramagnetic phase transition at $α\approx 0.94$. 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.

cond-mat.str-el↗
arXiv2020

On the theory of ideal Bose-gas at a finite particle number

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 $μ$ of the ideal Bose-gas can lie in the range $-\infty<μ<\infty$ oppositely to the widely adopted opinion that the value of this potential is negative.

cond-mat.stat-mech↗
arXiv2020

General solution of the Dirac equation with the Coulomb potential

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.

quant-ph↗
arXiv2020

Magnetorheological effect in elastomers containing uniaxial ferromagnetic particles

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.

cond-mat.soft↗
arXiv2020

Generalized spin-orbit interaction in two-dimensional electron systems

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.

cond-mat.mes-hall↗
arXiv2019

Effect of resonant impurity scattering of carriers on Drude peak broadening in uniaxially strained graphene

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.

cond-mat.dis-nn↗
arXiv2018

On the theory of high-$T_\text{c}$ superconductivity of doped cuprates

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.

cond-mat.supr-con↗
arXiv2017

On the theory of the Schroedinger equation with the full set of relativistic corrections

All relativistic corrections to the Scr{ö}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.

cond-mat.mes-hall↗
arXiv2015

General solution of the Dirac equation for quasi-two-dimensional electrons

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.

cond-mat.mes-hall↗
arXiv2015

Electric bias control on impurity effects in bigraphene

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.

cond-mat.dis-nn↗
arXiv2014

Spin states of Dirac equation and Rashba spin-orbit interaction

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.

cond-mat.mes-hall↗
arXiv2014

On the theory of inhomogeneous Bose-Einstein condensation of magnons in yttrium garnet

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.

cond-mat.quant-gas↗
arXiv2011

Density of states of relativistic and nonrelativistic two-dimensional electron gases in a uniform magnetic and Aharonov-Bohm fields

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 Schrödinger 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.

cond-mat.str-el↗