# Publications

Recently discussed topological materials Weyl-semimetals (WSs) combine both: high electron mobility comparable with graphene and unique topological protection of Dirac points. We present novel results related to electromagnetic field propagation through WSs. It is predicted that transmission of the normally incident polarized electromagnetic wave (EMW) through the magnetic WS strongly depends on the orientation of polarization with respect to a gyration vector g. The latter is related to the vector-parameter b, which represents the separation between the Weyl nodes of opposite chirality in the first Brillouin zone. By changing the polarization of the incident EMW with respect to the gyration vector g the system undergoes the transition from the isotropic dielectric to the medium with Kerr-or Faraday-like rotation of polarization and finally to the system with chiral selective electromagnetic field. It is shown that WSs can be applied as the polarization filters.

Throughout the years, strongly correlated coherent states of excitons have been the subject of intense theoretical and experimental studies. This topic has recently boomed due to new emerging quantum materials such as van der Waals (vdW) bound atomically thin layers of transition metal dichalcogenides (TMDs). We analyze the collective properties of charged interlayer excitons observed recently in bilayer TMD heterostructures. We predict strongly correlated phases – crystal and Wigner crystal – that can be selectively realized with TMD bilayers of properly chosen electron-hole effective masses by just varying their interlayer separation distance. Our results can be used for nonlinear coherent control, charge transport and spinoptronics application development with quantum vdW heterostuctures.

In this paper, we show how to construct an asymptotic representation of the fundamental solution to the Cauchy problem for degenerate linear parabolic equations.

Microcavity exciton-polaritons, known to exhibit nonequilibrium Bose condensation at high critical temperatures, can also be brought in thermal equilibrium with the surrounding medium and form a quantum degenerate Bose-Einstein distribution. It happens when their thermalization time in the regime of positive detunings – or, alternatively, for high-finesse microcavities – becomes shorter than their lifetime. Here we present the self-consistent finite-temperature Hartree–Fock–Bogoliubov description for such a system of polaritons, universally addressing the excitation spectrum, momentum-dependent interactions, condensate depletion, and the background population of dark excitons that contribute to the system’s chemical potential. Employing the derived expressions, we discuss the implications for the Bogoliubov sound velocity, confirmed by existing experiments, and define the critical temperatures of (quasi)condensation and the integral particle lifetime dependencies on the detuning. Large positive detunings are shown to provide conditions for the total lifetime reaching nanosecond timescales. This allows realization of *thermodynamically equilibrium *polariton systems with Bose-Einstein condensate forming at temperatures as high as tens of Kelvin.

A subsonic flow of a viscous compressible fluid in a two-dimensional channel with small periodic or localized irregularities on the walls for large Reynolds numbers is considered. A formal asymptotic solution with double-deck structure of the boundary layer is constructed. A nontrivial time hierarchy is discovered in the decks. An analysis of the scales of irregularities at which the double-deck structure exists is performed.

Confined modes at the edge arbitrarily inclined with respect to optical axes of nonmagnetic anisotropic 2D materials are considered. By developing the exact Wiener-Hopf and approximated Fetter methods we studied edge modes dispersions, field and charge density distributions. The 2D layer is described by the Lorentz-type conductivities in one or both directions, which is realistic for natural anisotropic 2D materials and resonant hyperbolic metasurfaces. We demonstrate that, due to anisotropy, the edge mode exists only at wave vectors exceeding the nonzero threshold value if the edge is tilted with respect to the direction of the resonant conductivity. The dominating contribution to field and charge density spatial profiles is provided by evanescent 2D waves, which are confined both in space near the 2D layer and along the layer near its edge. The degree of field confinement along the layer is determined by wave vector or frequency mismatch between the edge mode and continuum of freely propagating 2D modes. Our analysis is suitable for various types of polaritons (plasmon, phonon, exciton polaritons, etc.) at large enough wave vectors. Thanks to superior field confinement in all directions perpendicular to the edge these modes look promising for modern plasmonics and sensorics.

Ensembles with long-range interactions between particles are promising for revealing strong quantum collective effects and many-body phenomena. Here we study the ground-state phase diagram of a two-dimensional Bose system with quadrupolar interactions using a diffusionMonte Carlo technique. We predict a quantum phase transition from a gas to a solid phase. The Lindemann ratio and the condensate fraction at the transition point are *γ** *= 0*.*269(4) and *n*0*/**n *= 0*.*031(4), correspondingly. We observe the strong rotonization of the collective excitation branch in the vicinity of the phase transition point. Our results can be probed using state-of-the-art experimental systems of various nature, such as quasi-two-dimensional systems of quadrupolar excitons in transition metal dichalcogenide trilayers, quadrupolar molecules, and excitons or Rydberg atoms with quadrupole moments induced by strong magnetic fields.

The recent progress in nanotechnology1,2 and single-molecule spectroscopy3–5 paves the way for emergent cost-effective organic quantum optical technologies with potential applications in useful devices operating at ambient conditions. We harness a *π*-conjugated ladder-type polymer strongly coupled to a microcavity forming hybrid light–matter states, so-called exciton-polaritons, to create exciton-polariton condensates with quantum fluid properties. Obeying Bose statistics, exciton-polaritons exhibit an extreme nonlinearity when undergoing bosonic stimulation6, which we have managed to trigger at the single-photon level, thereby providing an efficient way for all-optical ultrafast control over the macroscopic condensate wavefunction. Here, we utilize stable excitons dressed with high-energy molecular vibrations, allowing for single-photon nonlinear operation at ambient conditions. This opens new horizons for practical implementations like sub-picosecond switching, amplification and all-optical logic at the fundamental quantum limit.

We report on structural and electronic properties of superconducting nanohybrids made of Pb grown in the ultrahigh vacuum on the atomically clean surface of single crystals of topological Bi2Te3. In situ scanning tunneling microscopy and spectroscopy demonstrated that the resulting network is composed of Pb-nanoislands dispersed on the surface and linked together by an amorphous atomic layer of Pb, which wets Bi2Te3. As a result, the superconducting state of the system is characterized by a thickness-dependent superconducting gap of Pb-islands and by a very unusual position-independent proximity gap between them. Furthermore, the data analysis and DFT calculations demonstrate that the Pb-wetting layer leads to significant modifications of both topological and trivial electronic states of Bi2Te3, which are responsible for the observed long-range proximity effect.

We report on structural and electronic properties of superconducting nanohybrids made of Pb grown in the ultrahigh vacuum on the atomically clean surface of single crystals of topological Bi2Te3. In situ scanning tunneling microscopy and spectroscopy demonstrated that the resulting network is composed of Pb-nanoislands dispersed on the surface and linked together by an amorphous atomic layer of Pb, which wets Bi2Te3. As a result, the superconducting state of the system is characterized by a thickness-dependent superconducting gap of Pb-islands and by a very unusual position-independent proximity gap between them. Furthermore, the data analysis and DFT calculations demonstrate that the Pb-wetting layer leads to significant modifications of both topological and trivial electronic states of Bi2Te3, which are responsible for the observed long-range proximity effect.

Molecular dynamics simulations show that a graphene nanoribbon with alternating regions which are one and three hexagons wide can transform into a hybrid 1D nanoobject with alternating double chains and polycyclic regions under electron irradiation in HRTEM. A scheme of synthesis of such a nanoribbon using Ullmann coupling and dehydrogenation reactions is proposed. The reactive REBO-1990EVC potential is adapted for simulations of carbon–hydrogen systems and is used in combination with the CompuTEM algorithm for modeling of electron irradiation effects. The atomistic mechanism of formation of the new hybrid 1D nanoobject is found to be the following. Firstly hydrogen is removed by electron impacts. Then spontaneous breaking of bonds between carbon atoms leads to the decomposition of narrow regions of the graphene nanoribbon into double chains. Simultaneously, thermally activated growth of polycyclic regions occurs. Density functional theory calculations give barriers along the growth path of polycyclic regions consistent with this mechanism. The electronic properties of the new 1D nanoobject are shown to be strongly affected by the edge magnetism and make this nanostructure promising for nanoelectronic and spintronic applications. The synthesis of the 1D nanoobject proposed here can be considered as an example of the general three-stage strategy of production of nanoobjects and macromolecules: (1) precursors are synthesized using a traditional chemical method, (2) precursors are placed in HRTEM with the electron energy that is sufficient only to remove hydrogen atoms, and (3) as a result of hydrogen removal, the precursors become unstable or metastable and transform into new nanoobjects or macromolecules.

We study the spectral problem for a two-dimensional Hartree type operator with smooth selfaction potential. We find

asymptotic eigenvalues and eigenfunctions and construct an asymptotic expansion for quantum averages near

the lower boundaries of spectral clusters.

The scheme and operational principles of graphene-based nanoelectromechanical system (NEMS) for study of interaction between graphene and surface of a sample is proposed. In such a NEMS multilayer graphene membrane bends due to van der Waals attraction between surface of graphene membrane and surface of a sample attached to a manipulator. An analysis of the NEMS total energy balance shows that the NEMS is bistable and abrupt transition between the stable states occurs if the sample is moved toward and backward the membrane. The detection of the interface distances corresponding to these transitions can be used to fit parameters of interatomic potentials for interaction between atoms of the surfaces of the graphene membrane and the sample. The analytical expression for dependences of this transition distances on NEMS sizes and parameters of the potential are derived on example of Lennard-Jones potential. For graphene-graphene interaction the transition distance is estimated to be from several nanometers to several tens nanometers for possible sizes of the proposed NEMS and thus can be measurable for example by transmission electron microscopy. Possibility of this NEMS implementation and application to study graphene-metal interaction are discussed.

Formation of exciton-polariton condensate due to incoherent pumping of an excitonic reservoir is considered. The condensate dynamics is governed by a system of stochastic integro-differential equations of Langevin's type corresponding to the model developed by Elistratov and Lozovik [12]. Attention is concentrated on non-Markovian interaction of the condensate with the excitonic and photonic reservoirs. It is shown that dynamical memory caused by the non-Markovian interaction qualitatively changes the condensate behavior as compared to the Markovian regime. In particular, it diminishes the threshold of pumping strength for the condensate emergence. Also, it is found that the non-Markovian regime leads to relaxation oscillations corresponding to population exchange between the condensate and the excitonic reservoir. Increasing of incoherent pumping strength leads to chaos of relaxation oscillations that is accompanied by random-like transitions between the lower and upper polaritonic states.

A problem with free (unknown) boundary for a one-dimensional diffusion-convection equation is considered. The unknown boundary is found from an additional condition on the free boundary. By the extension of the variables, the problem in an unknown domain is reduced to an initial boundary-value problem for a strictly parabolic equation with unknown coefficients in a known domain. These coefficients are found from an additional boundary condition that enables the construction of a nonlinear operator whose fixed points determine a solution of the original problem.

We study the effect of interlayer Coulomb interaction in an electronic double layer. Assuming that each of the layers consists of a bipartite lattice, a sufficiently strong interlayer interaction leads to an interlayer pairing of electrons with a staggered order parameter. We show that the correlated pairing state is dual to the excitonic pairing state with a uniform order parameter in an electron-hole double layer. The interlayer pairing of electrons leads to strong current-current correlations between the layers. We also analyze the interlayer conductivity and the fluctuations of the order parameter, which consists of a gapped and a gapless mode.

Using semion substitution for spin variables we perform an *ab initio* derivation of effective action for an open quantum two-level system . For this purpose, we introduce, by using the Hubbard-Stratonovich transformation a two-time complex quantum field which average value plays the role of the Green's function for the spin variables. The field thus introduced allows us to develop a diagram technique in a standard way. The proposed formalism is used to study a spin embedded into an Ohmic reservoir as an example of the spin-boson model. Non-Markovian effects in this system are analyzed.

Using semion substitution for spin variables we perform an ab initio derivation of effective action for an open quantum two-level system. For this purpose, we introduce, by using the Hubbard-Stratonovich transformation a two-time complex quantum field which average value plays the role of the Green's function for the spin variables. The field thus introduced allows us to develop a diagram technique in a standard way. The proposed formalism is used to study a spin embedded into an Ohmic reservoir as an example of the spin-boson model. Non-Markovian effects in this system are analyzed.

We consider the homogenization of diffusion-convective problems with given divergence-free velocities in nonperiodic structures defined by sequences of characteristic functions the first sequence . These quence of concentration the second sequence is uniformly bounded in the space of square-summable functions with square-summable derivatives with respect to spatial variables. At the same time, the sequence of time-derivative of product of these concentrations on the characteristic functions, that define a nonperiodic structure, is bounded in the space of square-summable functions from time interval into the conjugated space of functions depending on spatial variables, withsquare-summable derivatives. We prove the strong compactness of the second sequences in the space of quadratically summable functions and use this result to homogenize the corresponding boundary value problems that depend on a small parameter.

In view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) nonstationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields, and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of a generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and numbers of two-level systems are finite. In this case, the superradiant quantum phase transition is changed to a fluctuational region in the phase diagram that reveals two types of critical behaviors. These are regimes of Dicke model (with discrete Z2 symmetry), and that of anti-Tavis-Cummings and Tavis-Cummings U(1) models. We show that squeezing parameters of photon condensate in these regimes show distinct temperature scalings. Besides, relative fluctuations of a photon number take universal values. We also find a temperature scale below which one approaches a zero-temperature quantum phase transition where quantum fluctuations dominate. Our effective theory is provided by a non-Goldstone functional for condensate mode and by Majorana representation of Pauli operators. We also discuss the Bethe ansatz solution for integrable U(1) limits.

In view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) nonstationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields, and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of a generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and numbers of two-level systems are finite. In this case, the superradiant quantum phase transition is changed to a fluctuational region in the phase diagram that reveals two types of critical behaviors. These are regimes of Dicke model (with discrete Z2 symmetry), and that of anti-Tavis-Cummings and Tavis-Cummings U(1) models. We show that squeezing parameters of photon condensate in these regimes show distinct temperature scalings. Besides, relative fluctuations of a photon number take universal values. We also find a temperature scale below which one approaches a zero-temperature quantum phase transition where quantum fluctuations dominate. Our effective theory is provided by a non-Goldstone functional for condensate mode and by Majorana representation of Pauli operators. We also discuss the Bethe ansatz solution for integrable U(1) limits.