arXiv subjects

M. A. Zubkov

Publications and source records attributed to M. A. Zubkov.

At least 55 records · Page 3Linked to original sources

arXiv2021

Wigner transformation, momentum space topology, and anomalous transport

Using derivative expansion applied to the Wigner transform of the two - point Green function we analyse the anomalous quantum Hall effect (AQHE), and the chiral magnetic effect (CME). The corresponding currents are proportional to the momentum space topological invariants. We reproduce the conventional expression for the Hall conductivity in $2+1$ D. In $3+1$ D our analysis allows to explain systematically the AQHE in topological insulators and Weyl semimetals. At the same time using this method it may be proved, that the equilibrium CME is absent in the wide class of solids, as well as in the properly regularized relativistic quantum field theory.

cond-mat.mes-hall↗

arXiv2021

Influence of interactions on the anomalous quantum Hall effect

The anomalous quantum Hall conductivity in the 2+1D topological insulators in the absence of interactions may be expressed as the topological invariant composed of the two - point Green function. For the noninteracting system this expression is the alternative way to represent the TKNN invariant. It is widely believed that in the presence of interactions the Hall conductivity is given by the same expression, in which the noninteracting two - point Green function is substituted by the complete two - point Green function with the interactions taken into account. However, the proof of this statement has not been given so far. In the present paper we give such a proof in the framework of the particular tight - binding models of the $2+1$ D topological insulator. Besides, we extend our consideration to the $3+1$ D Weyl semimetals. It was known previously that with the interactions neglected the Hall conductivity in those systems is expressed through the two - point Green function in the way similar to that of the $2+1$ D topological insulators. Again, the influence of interactions on this expression has not been investigated previously. We consider this problem within the framework of the particular $3+1$D model of Weyl semimetal in the presence of the contact four - fermion interactions and Coulomb interactions. We prove (up to the one - loop approximation), that the Hall conductivity is given by the same expression as in the noninteracting case, in which the noninteracting Green function is substituted by the complete two - point Green function with the interactions included. Basing on the obtained expressions we discuss the topological phase transitions accompanied by the change of Hall conductivity.

cond-mat.mes-hall↗

arXiv2021

Topological invariant in terms of the Green functions for the Quantum Hall Effect in the presence of varying magnetic field

Recently the Wigner - Weyl formalism has been applied to the lattice models of solid state physics and to the lattice regularized quantum field theory. This allows to demonstrate that the electric current of intrinsic Anomalous Quantum Hall effect is expressed through the momentum space topological invariant composed of the Green functions both for the two - and the three - dimensional systems. Here we extend this consideration to the case of the Quantum Hall Effect existing in the presence of arbitrarily varying external magnetic field. The corresponding electric current appears to be proportional to the topological invariant in phase space composed of the Wigner transformed Green function that depends both on coordinates and momenta.

cond-mat.mes-hall↗

arXiv2021

Wigner-Weyl calculus in Keldysh technique

We discuss the non-equilibrium dynamics of condensed matter/quantum field systems in the framework of Keldysh technique. In order to deal with the inhomogeneous systems we use the Wigner-Weyl formalism. Unification of the mentioned two approaches is demonstrated on the example of Hall conductivity. We express Hall conductivity through the Wigner transformed two-point Green's functions. We demonstrate how this expression is reduced to the topological number in thermal equilibrium at zero temperature. At the same time both at finite temperature and out of equilibrium the topological invariance is lost. Moreover, Hall conductivity becomes sensitive to interaction corrections.

cond-mat.mes-hall↗

arXiv2020

Abelian Fock-Schwinger representation for the quark propagator in external gauge field

We develop the Diakonov-Petrov approach to the representation of the non-Abelian Wilson loop in an Abelian form. First of all, we extend this approach to the Abelian representation of the parallel transporter corresponding to the open curve rather than to the closed contour. Next, we extend this representation to the case of the non-compact groups. The obtained expressions allow to derive the Abelian form of the Schwinger-Fock representation for the quark propagator in an external color gauge field.

hep-ph↗

arXiv2020

High energy scattering in Einstein-Cartan gravity

We consider Riemann-Cartan gravity with minimal Palatini action, which is classically equivalent to Einstein gravity. Following the ideas of L.Lipatov \cite{LipGrav} we propose the effective action for this theory aimed at the description of the high-energy scattering of gravitating particles in the multi - Regge kinematics. For that purpose we add to the Palatini action the new terms responsible for the interaction of gravitational quanta with certain collective excitations that replace exchange by multiple gravitational excitations. We propose the heuristic explanation of its particular form based on an analogy to the reggeon field theory of QCD. We argue that Regge kinematics assumes the appearance of an effective two - dimensional model describing the high - energy scattering similar to that of QCD. Such a model may be formulated in a way leading to our final effective theory, which contains interaction between the ordinary quanta of spin connection and vielbein with their effective counterparts that pretend to the role of the gravitational reggeons.

hep-th↗

arXiv2020

Chiral Separation effect in non-homogeneous systems

We discuss chiral separation effect in the systems with spatial non - homogeneity. It may be caused by non - uniform electric potential or by another reasons, which do not, however, break chiral symmetry of an effective low energy theory. Such low energy effective theory describes quasiparticles close to the Fermi surfaces. In the presence of constant external magnetic field the non - dissipative axial current appears. It appears that its response to chemical potential and magnetic field (the CSE conductivity) is universal. It is robust to smooth modifications of the system and is expressed through an integral over a surface in momentum space that surrounds all singularities of the Green function. In itself this expression represents an extension of the topological invariant protecting Fermi points to the case of inhomogeneous systems.

hep-th↗

arXiv2020

RF-coil with variable resonant frequency for multiheteronuclear ultra-high field MRI

Here we propose double-coil setup to allow high signal-to-noise ratio broad-range heteronuclear magnetic resonance imaging experiments: two independent coils, one of them tuned to $^{1}$H frequency to perform anatomical $^{1}$H imaging, and another one, metamaterial-inspired coil, tuned to the X-nucleus frequency. In this work our goal was to design a broad-range X-nuclei coil to cover $^{2}$H, $^{11}$B, $^{13}$C, $^{23}$Na, $^{7}$Li and $^{31}$P nuclear magnetic resonance frequencies, and to combine it with $^{1}$H coil in one setup. The system was designed for 11.7 T scanner, i.e., with 76-203 MHz frequency tuning range for the X-nuclei and tuned to 500 MHz for the proton coil. X-nuclei coil operates via excitation of the fundamental eigenmode of an array of parallel non-magnetic wires. The excitation of the array is provided via non-resonant feeding loop inductively coupled to the resonator. In order to tune the X-coil over such a wide range, both structural capacitance and inductance of the coil were made variable; narrow range tuning of the $^{1}$H coil is achieved via conventional tuning-matching circuit. Here, the design principle and setup tunability were investigated in simulations and experimentally.

physics.med-ph↗

arXiv2020

Quantum Hall conductivity in the presence of interactions

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over the ground state of the system. This conclusion remains valid for both integer and fractional quantum Hall effect.

cond-mat.mes-hall↗

arXiv2020

Feynman Rules in terms of the Wigner transformed Green functions

In the models defined on the inhomogeneous background the propagators depend on the two space - time momenta rather than on one momentum as in the homogeneous systems. Therefore, the conventional Feynman diagrams contain extra integrations over momenta, which complicate calculations. We propose to express all amplitudes through the Wigner transformed propagators. This approach allows us to reduce the number of integrations. As a price for this the ordinary products of functions are replaced by the Moyal products. The corresponding rules of the diagram technique are formulated using an example of the model with the fermions interacting via an exchange by scalar bosons. The extension of these rules to the other models is straightforward. This approach may simplify calculations in certain particular cases. The most evident one is the calculation of various non - dissipative currents.

hep-ph↗

arXiv2019

A Note on Bloch theorem

Bloch theorem in ordinary quantum mechanics means the absence of the total electric current in equilibrium. In the present paper we analyze the possibility that this theorem remains valid within quantum field theory relevant for the description of both high energy physics and condensed matter physics phenomena. First of all, we prove that the total electric current in equilibrium is the topological invariant for the gapped fermions that are subject to periodical boundary conditions, i.e. it is robust to the smooth modification of such systems. This property remains valid when the inter - fermion interactions due to the exchange by bosonic excitations are taken into account perturbatively. We give the proof of this statement to all orders in perturbation theory. Thus we prove the weak version of the Bloch theorem, and conclude that the total current remains zero in any system, which is obtained by smooth modification of the one with the gapped charged fermions, periodical boundary conditions, and vanishing total electric current. We analyse several examples, in which the fermions are gapless. In some of them the total electric current vanishes. At the same time we propose the counterexamples of the equilibrium gapless systems, in which the total electric current is nonzero.

cond-mat.mes-hall↗

arXiv2019

Precise Wigner-Weyl calculus for lattice models

We propose a new version of Wigner-Weyl calculus for tight-binding lattice models. It allows to express various physical quantities through Weyl symbols of operators and Green's functions. In particular, Hall conductivity in the presence of varying and arbitrarily strong magnetic field is represented using the proposed formalism as a topological invariant.

math-ph↗

arXiv2019

Hall conductivity of strained $Z_2$ crystals

We establish topological nature of Hall conductivity of graphene and other $Z_2$ crystals in 2D and 3D in the presence of inhomogeneous perturbations. To this end the lattice Weyl-Wigner formalism is employed. The non-uniform mechanical stress is considered, along with spatially varying magnetic field. The relation of the obtained topological invariant to level counting is clarified.

cond-mat.mes-hall↗

arXiv2019

Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field

The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently the generalization of this expression has been proposed for the non - uniform magnetic field. \rev{The quantum Hall conductivity is represented as the topological invariant in phase space in terms of the Wigner transformed two - point Green function.} This representation has been derived when the inter - electron interactions were neglected. It is natural to suppose, that in the presence of interactions the Hall conductivity is still given by the same expression, in which the non - interacting Green function is substituted by the complete two - point Green function \rev{ including the interaction contributions}. We prove this conjecture within the framework of the $2+1$ D tight - binding model of rather general type using the ordinary perturbation theory.

cond-mat.mes-hall↗

arXiv2019

Classical limit for Dirac fermions with modified action in the presence of the black hole

We consider the model of Dirac fermions coupled to gravity as proposed in \cite{VolovikBH}, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics. Due to this term a closed Fermi surface is formed in equilibrium inside the black hole. In this paper we propose the covariant formulation of this model and analyse its classical limit. We consider the dynamics of gravitational collapse. It appears that the Einstein equations admit a solution identical to that of the ordinary general relativity. Next, we consider motion of particles in the presence of the black hole. Numerical solutions of the equations of motion are found which demonstrate that the particles are able to escape from the black hole.

gr-qc↗

arXiv2019

Elastic deformations and Wigner-Weyl formalism in graphene

We discuss the tight-binding models of solid state physics with the $Z_2$ sublattice symmetry in the presence of elastic deformations, and their important particular case -the tight binding model of graphene. In order to describe the dynamics of electronic quasiparticles we explore Wigner-Weyl formalism. It allows to calculate the two-point Green's function in the presence of both slowly varying external electromagnetic fields and the inhomogeneous modification of the hopping parameters resulted from the elastic deformations. The developed formalism allows us to consider the influence of elastic deformations and the variations of magnetic field on the quantum Hall effect.

cond-mat.mes-hall↗

arXiv2018

Chiral torsional effect

We propose the new nondissipative transport effect - the appearance of axial current of thermal quasiparticles in the presence of background gravity with torsion. For the non-interacting model of massless Dirac fermions the response of the axial current to torsion is derived. The chiral vortical effect appears to be the particular case of the chiral torsional effect. The proposed effect may be observed in the condensed matter systems with emergent relativistic invariance (Weyl/Dirac semimetals and the $^3$He-A superfluid).

cond-mat.mes-hall↗

arXiv2018

Analogies between the Black Hole Interior and the Type II Weyl Semimetals

In the Painleve--Gullstrand (PG) reference frame, the description of elementary particles in the background of a black hole (BH) is similar to the description of non-relativistic matter falling toward the BH center. The velocity of the fall depends on the distance to the center, and it surpasses the speed of light inside the horizon.~Another analogy to non-relativistic physics appears in the description of the massless fermionic particle. Its Hamiltonian inside the BH, when written in the PG reference frame, is identical to the Hamiltonian of the electronic quasiparticles in type~II Weyl semimetals (WSII) that reside in the vicinity of a type~II Weyl point. When these materials are in the equilibrium state, the type II Weyl point becomes the crossing point of the two pieces of the Fermi surface called Fermi pockets. {It was previously stated} that there should be a Fermi surface inside a black hole in equilibrium. In real materials, type II Weyl points come in pairs, and the descriptions of the quasiparticles in their vicinities are, to a certain extent, inverse. Namely, the directions of their velocities are opposite. In line with the mentioned analogy, we propose the hypothesis that inside the equilibrium BH there exist low-energy excitations moving toward the exterior of the BH. These excitations are able to escape from the BH, unlike ordinary matter that falls to its center. The important consequences to the quantum theory of black holes follow.

gr-qc↗