arXiv subjects

V. P. Gusynin

Publications and source records attributed to V. P. Gusynin.

At least 19 recordsLinked to original sources

arXiv2026

Nodal structure of bound-state wave functions for systems with quartic dispersion

The nodal structure of bound-state wave functions for one-dimensional quantum systems with quartic energy-momentum dispersion and polynomial potentials is analysed by using the semiclassical approximation and variational approach. For energies of bound states, we derive the quantization condition, obtained by using the complex Wentzel method, where we take into account perturbative (up to the fourth order) and nonperturbative in the Planck constant corrections. The bound-state energies and wave functions for the harmonic and quartic potentials are compared with those found by applying the variational approach utilizing the universal Gaussian basis. It is shown that the classical oscillation theorem, valid for systems with quadratic energy-momentum dispersion, breaks down in the classically forbidden region where wave functions also have nodes, while it still remains valid in the classically allowed region. These results are confirmed in addition via the solutions of the exactly solvable problem of the fourth-order Schrodinger equation with a square well potential.

cond-mat.str-el↗

arXiv2025

Bound states of quasiparticles with quartic dispersion in an external potential: WKB approach

The Wentzel-Kramers-Brillouin semiclassical method is formulated for quasiparticles with quartic-in-momentum dispersion which presents the simplest case of a soft energy-momentum dispersion. It is shown that matching wave functions in the classically forbidden and allowed regions requires the consideration of higher-order Airy-type functions. The asymptotics of these functions are found by using the method of steepest descents and contain additional exponentially suppressed contributions known as hyperasymptotics. These hyperasymptotics are crucially important for the correct matching of wave functions in vicinity of turning points for higher-order differential equations. A quantization condition for bound state energies is obtained, which generalizes the standard Bohr-Sommerfeld quantization condition for particles with quadratic energy-momentum dispersion and contains non-perturbative in $\hbar$ correction. This non-perturbative correction, usually associated with tunneling effects or the presence of complex turning points, occurs even for the harmonic potential with quartic dispersion where complex turning points and tunneling are absent. The quantization condition is used to find bound state energies in the case of quadratic and quartic potentials.

cond-mat.str-el↗

arXiv2025

RKKY quadratic and biquadratic spin-spin interactions in twisted bilayer graphene

We study the competition between the RKKY quadratic and biquadratic spin-spin interactions of two magnetic impurities in twisted bilayer graphene away from the magic angle. We apply the Bistritzer-MacDonald model of two graphene layers twisted with respect to each other by a small angle. By reducing the model to the Dirac-type one with modified Fermi velocity, we derive expressions for the RKKY quadratic and biquadratic spin interactions using perturbation theory for the free energy. The biquadratic interaction is suppressed by a larger power of the interaction constant and decreases faster with a the distance between impurities comparing to the quadratic one. Nevertheless, due to the different period of oscillations with impurity separation distance, chemical potential, twist angle and temperature, it is possible to fine-tune the system to the regime of dominating biquadratic interaction. The existence of such fine-tuned regime might provide a promising opportunity to observe non-conventional spin ordering.

cond-mat.mes-hall↗

arXiv2025

WKB energy levels in gapped graphene under crossed electromagnetic fields

We consider a single layer of graphene subjected to a magnetic field $H$ applied perpendicular to the layer and an in-plane constant radial electric field $E$. The Dirac equation for this configuration does not admit analytical solutions in terms of known special functions. Using the WKB approximation, we demonstrate that for gapped graphene the Bohr-Sommerfeld quantization condition for eigenenergies includes an additional valley-dependent geometrical phase. When this term is accounted for, the WKB approximation exhibits good agreement with results from the exact diagonalization method except to the lowest Landau level.

cond-mat.mes-hall↗

arXiv2024

Peculiarities of the Landau level collapse in graphene ribbons in crossed magnetic and in-plane electric fields

Employing the low-energy effective theory alongside a combination of analytical and numerical techniques, we explore the Landau level collapse phenomenon, uncovering previously undisclosed features. We consider both finite-width graphene ribbons and semi-infinite geometries subjected to a perpendicular magnetic field and an in-plane electric field, applied perpendicular to both zigzag and armchair edges. In the semi-infinite geometry the hole (electron)-like Landau levels collapse as the ratio of electric and magnetic fields reaches the critical value $ +(-) 1$. On the other hand, the energies of the electron (hole)-like levels remain distinct near the edge and deeply within the bulk approaching each other asymptotically for the same critical value. In the finite geometry, we show that the electron (hole)-like levels become denser and merge, forming a band.

cond-mat.mes-hall↗

arXiv2024

Reduced QED with few planes and fermion gap generation

The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of few atomically thick layers and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced theory describes charged fermions confined to $N$ planes and contains $N$ vector fields with Maxwell`s action modified by non-local form factors whose explicit form is determined. Taking into account the polarization function, the explicit formulae for the screened electromagnetic interaction are presented in the case of two and three layers. For a heterostructure with two atomically thick layers and charged fermions described by the massless Dirac equation, the dynamical gap generation of the excitonic type is studied. It is found that additional screening due to the second layer increases the value of the critical coupling constant for the gap generation compared to that in graphene.

cond-mat.str-el↗

arXiv2024

Electron binding energy of a donor in bilayer graphene with gate-tunable gap

In gapped bilayer graphene, similarly to conventional semiconductors, Coulomb impurities (such as nitrogen donors) may determine the activation energy of its conductivity and provide low temperature hopping conductivity. However, in spite of the importance of Coulomb impurities, nothing is known about their electron binding energy $E_b$ in the presence of gates. To close this gap, we study numerically the electron binding energy $E_b$ of a singly charged donor in BN-enveloped bilayer graphene with the top and bottom gates at distance $d$ and gate-tunable gap $2Δ$. We show that for $10 < d < 200$ nm and $1 < Δ< 100$ meV the ratio $E_b/Δ$ changes from 0.4 to 1.5. The ratio $E_b/Δ$ stays close to unity because of the dominating role of the bilayer polarization screening which reduces the Coulomb potential well depth to values $\sim Δ$. Still the ratio $E_b/Δ$ somewhat decreases with growing $Δ$, faster at small $Δ$ and slower at large $Δ$. On the other hand, $E_b/Δ$ weakly grows with $d$, again faster at small $Δ$ and slower at large $Δ$. We also studied the effect of trigonal warping and found only a small reduction of $E_b/Δ$.

cond-mat.mes-hall↗

arXiv2023

Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian

The spectrum of a one-dimensional pseudospin-one Hamiltonian with a three-component potential is studied for two configurations: (i) all the potential components are constants over the whole coordinate space and (ii) the profile of some components is of a rectangular form. In case (i), it is illustrated how the structure of three (lower, middle and upper) bands depends on the configuration of potential strengths including the appearance of flat bands at some special values of these strengths. In case (ii), the set of two equations for finding bound states is derived. The spectrum of bound-state energies is shown to depend crucially on the configuration of potential strengths. Each of these configurations is specified by a single strength parameter $V$. The bound-state energies are calculated as functions of the strength $V$ and a one-point approach is developed realizing correspondent point interactions. For different potential configurations, the energy dependence on the strength $V$ is described in detail, including its one-point approximation. From a whole variety of bound-state spectra, four characteristic types are singled out.

quant-ph↗

arXiv2023

Bound states of a one-dimensional Dirac equation with multiple delta-potentials

Two approaches are developed for the study of the bound states of a one-dimensional Dirac equation with the potential consisting of $N$ $δ$-function centers. One of these uses the Green's function method. This method is applicable to a finite number $N$ of $δ$-point centers, reducing the bound state problem to finding the energy eigenvalues from the determinant of a $2N\times2N$ matrix. The second approach starts with the matrix for a single delta-center that connects the two-sided boundary conditions for this center. This connection matrix is obtained from the squeezing limit of a piecewise constant approximation of the delta-function. Having then the connection matrices for each center, the transmission matrix for the whole system is obtained by multiplying the one-center connection matrices and the free transfer matrices between neighbor centers. An equation for bound state energies is derived in terms of the elements of the total transfer matrix. Within both the approaches, the transcendental equations for bound state energies are derived, the solutions to which depend on the strength of delta-centers and the distance between them, and this dependence is illustrated by numerical calculations. The bound state energies for the potentials composed of one, two, and three delta-centers ($N=1,\,2,\,3$) are computed explicitly. The principle of strength additivity is analyzed in the limits as the delta-centers merge at a single point or diverge to infinity.

quant-ph↗

arXiv2023

Zigzag edge states in graphene in the presence of in-plane electric field

The present study explores the edge states in a finite-width graphene ribbon and a semi-infinite geometry subject to a perpendicular magnetic field and an in-plane electric field, applied perpendicular to a zigzag edge. To accomplish this, a combination of analytic and numerical methods within the framework of low-energy effective theory is employed. Both the gapless and gapped Dirac fermions in graphene are considered. It is found that a surface mode localized at the zigzag edge remains dispersionless even in the presence of electric field. This is shown analytically by employing Darwin's expansion of the parabolic cylinder functions of large order and argument.

cond-mat.mes-hall↗

arXiv2022

Landau level collapse in graphene in the presence of in-plane radial electric and perpendicular magnetic fields

It is known that in two-dimensional relativistic Dirac systems placed in orthogonal uniform magnetic and electric fields, the Landau levels collapse as the applied in-plane electric field reaches a critical value $\pm E_c$. We study this phenomenon for a distinct field configuration with in-plane constant radial electric field. The Dirac equation for this configuration does not allow analytical solutions in terms of known special functions. The results are obtained by using both the WKB approximation and the exact diagonalization and shooting methods. It is shown that the collapse occurs for positive values of the total angular momentum quantum number, the hole (electron)-like Landau levels collapse as the electric field reaches the value $ +(-) E_c/2$. The investigation of the Landau level collapse in the case of gapped graphene shows a number of distinctive features in comparison with the gapless case.

cond-mat.mes-hall↗

arXiv2022

Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach

We present a method to calculate the optical conductivity of semi-Dirac and pseudospin models based on the evaluation of quasiparticle velocity correlators which also describe the phenomenon of zitterbewegung. Applying this method to the semi-Dirac model with merging Dirac cones and gapped dice and Lieb lattice models we find exact analytical expressions for optical longitudinal and Hall conductivities. For the semi-Dirac model the obtained expressions allow us to analyze the role of spectrum anisotropy, van Hove singularities and Dirac cones in longitudinal conductivity. In addition, we predict signatures of topological phase transition with changing gap parameter in such a system that are manifested in dc transport at low temperatures. For the dice and Lieb lattices we emphasize the role of spectral gap, which defines frequency thresholds related to transitions to and from flat band.

cond-mat.str-el↗

arXiv2021

Genesis and fading away of persistent currents in a Corbino disk geometry

The detailed analytical and numerical analysis of the electron spectrum, persistent currents, and their densities for an annulus placed in a constant magnetic field (Corbino disk geometry) is presented. We calculate the current density profiles and study their dependence on the inner and outer radii of the annular. We study evolution of the persistent currents and track their emergence and decay for different limiting cases of such a geometry, starting from a nanodot and ending by a macroscopic circle. Our analytical results for the currents are confirmed by the agreement between the integration of the corresponding current densities and the application of the Byers-Yang formula, when it is applicable. Among other results we find the general expression for the persistent current in a narrow annulus, which in the one channel approximation reproduces the well-known result for quasi-one dimensional mesoscopic metallic ring. Moreover it allows to analyze the multi-channel case of a relatively wide annulus. Our study can be used for more accurate treatment and interpretation of the experimental data with measurements of the persistent currents in different doubly-connected systems.

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↗

arXiv2021

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

The gap generation in the dice model with local four-fermion interaction is studied. Due to the presence of two valleys with degenerate electron states, there are two main types of gaps. The intra- and intervalley gap describes the electron and hole pairing in the same and different valleys, respectively. We found that while the generation of the intravalley gap takes place only in the supercritical regime, the intervalley gap is generated for an arbitrary small coupling. The physical reason for the absence of the critical coupling is the catalysis of the intervalley gap generation by the flat band in the electron spectrum of the dice model. The completely quenched kinetic energy in the flat band when integrated over momentum in the gap equation leads to extremely large intervalley gap proportional to the area of the Brillouin zone.

cond-mat.str-el↗

arXiv2020

Four-loop singularities of the massless fermion propagator in quenched three-dimensional QED

We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation.

hep-th↗

arXiv2020

Landau-Khalatnikov-Fradkin transformation in three-dimensional quenched QED

We study the gauge-covariance of the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics in the framework of dimensional regularization in d=3-2\ep. Assuming the finiteness of the quenched perturbative expansion, that is the existence of the limit \ep \to 0, we state that, exactly in d=3, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge.

hep-th↗

arXiv2020

RKKY interaction in a doped pseudospin-1 fermion system at finite temperature

We study the RKKY interaction of magnetic impurities in the $α-\mathcal{T}_3$ model which hosts pseudospin-1 fermions with two dispersive and one flat bands. By using the effective low-energy Hamiltonian we calculate the RKKY coupling for impurities placed on the same or different sublattices. We find that there are three types of interaction, which depend on the model parameter defining the relative strength of hoppings between sublattices, two of them can be reduced to graphene case while the third one is new and is due to the presence of a flat zero-energy band. We derive general analytical expressions for the RKKY interaction in terms of Mellin-Barnes type integrals and analyze different limiting cases. The cases of finite chemical potential and temperature, as well as asymptotic at large distances are considered. We show that the interaction between impurities located at different rim sites displays a very strong temperature dependence at small doping being a direct consequence of the flat band. The subtleties of the theorem for signs of the RKKY interaction at zero doping, as applied to the $\mathcal{T}_3$ lattice, related to the existence of a dispersionless flat band are discussed.

cond-mat.str-el↗