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[en] The thermodynamic properties of a cluster of point Coulomb charges on a sphere have been analyzed using the Monte Carlo method for the number of charges 20 ≤ N ≤ 90. The ground state of the system of charges is described in the model of a closed quasi-two-dimensional triangular lattice with topological defects. We have determined the dependence of the Lindeman parameter δ_L of this system on N and on the dimensionless parameter, which is proportional to the temperature T and to the radius R of the cluster, where element is the dielectric constant of the medium and the charge of a particle. The 'magic numbers,' i.e., the N values, for which the melting point of the closed triangular lattice of charges is much higher than those for neighboring N values, have been found. The evolution of the lattice-melting mechanisms with an increase in the number of charges N in a mesoscopic cluster has been analyzed. For N ≤ 32, the melting of the lattice does not involve dislocations (nontopological melting); this behavior of the mesoscopic system of charges on the sphere differs from the behavior of the extended planar two-dimensional system. At N ≥ 50, melting is accompanied by the formation of dislocations. The mechanism of dislocation-free non-topological melting of a closed lattice, which occurs at small N values and is associated with the cooperative rotational motion of 'rings' of particles, has been analyzed. The model has various implementations in the mesoscopic region; in particular, it describes the system of electrons over the liquid-helium cluster, the liquid-helium cluster with incorporated charged particles, a multielectron bubble in liquid helium, a charged quantum dot, etc.

[en] New effects in systems of excitons in novel two-dimensional (2D) materials and structures [1-4] reviewed (see also [5] and refs therein). We propose a method to increase the lifetime of 2D direct excitons by optical cavity engineering and show the possibility to observe their macroscopically coherent state at temperatures much higher than that of indirect exciton condensation [1]. For 2D material or quantum well embedded in photonic layered heterostructures with subwavelength period, we predict the exciton radiative decay to be strongly suppressed. We propose the method to study dark 2D excitons (e.g. in 2D TMDC) by neighboring bright excitons in the neighboring layer [2]. We demonstrate that the interlayer interaction leads to a mixing between excitations from different layers which leads to the appearance of a second spectral branch in the spectrum of bright condensate. The excitation spectrum of the condensate of dark dipolar excitons then becomes optically accessible by luminescence of the bright condensate. We propose to control of electron-hole superfluidity in double layers of 2D material by an external periodic potential [3]. The second order phase transition between superfluid and electron-hole plasma, controlled by the external periodic potential, is studied. We predict the spin Hall effect for polaritons in 2D TMDC embedded in a microcavity [4]. A and B polaritons is formed due to the coupling of A and B excitons created in a TMDC monolayer and microcavity photons. Two counter propagating laser beams incident on a TMDC monolayer can split normal and superfluid polariton flows due to the generation the spin-dependent gauge magnetic and electric fields. We show that the polariton flows in the same valley are splitting: the superfluid components of the A and B polariton flows propagate in opposite directions along the counter propagating beams, while their normal components flows almost perpendicularly to the superfluid flows.

[en] A system of like (positive or negative) charges forming 'snowballs' or 'bubbles' in a three-dimensional liquid helium cluster is investigated. The charges are confined inside the cluster by an 'image potential' produced by the polarization of liquid helium. The stability of a multiply charged helium cluster is considered. Computer simulations are used to investigate the crystallization and melting of the system of charges depending on the dimensionless parameter T* = k_BTεR/e², where k_B is the Boltzmann constant, T is the temperature, ε is the dielectric constant of liquid helium, R is the cluster radius, and e is a unit charge. Various characteristics, including symmetry groups and moments, have been found for equilibrium configurations of charges in a cluster with N = 1-100 charges. At small N ∼ 10, Thomson's model of successive filling of 'belts' of charges can be used to describe the structure of equilibrium configurations of charges. At large N, the description of the structure formed by charges using the idea of a quasi-two-dimensional 'closed triangular lattice' with topological defects is more adequate. Formally, this description is valid starting from N = 4. The melting of a 'lattice' of charges is described. A number of our conclusions can be generalized to clusters of other noble gases

[en] Unique band structure peculiarities of graphene imply that near Fermi level electrons are effectively described by two-dimensional Dirac equation for massless particles. We investigate how these peculiarities manifest in electron-hole pairing and properties of indirect magnetoexcitons in two spatially separated, independently gated graphene layers. We study electron-hole pairing in weak-coupling regime, find the gap in energy spectrum and discuss system behavior at various controlling parameters. In case of extremely strong coupling, we show that localized electron-hole pairs are absent in graphene, and thus a behavior of graphene bilayer versus coupling strength is cardinally different from crossover to local pairs in usual Fermi systems. We discuss spectroscopy of indirect magnetoexcitons in graphene and possibility of their superfluidity. The systems under consideration can reveal coherent properties, dissipationless currents and Josephson-like phenomena at room temperature.

[en] Properties of collective excitonic and plasmonic excitations on the surface of three-dimensional topological insulator are reviewed. Due to spin-momentum locking for electrons populating the surface states plasmonic excitation manifests itself as coupled spin- and density-wave and can be called 'spin-plasmon'. Its excitation induces spin polarization of topological insulator surface that is perpendicular to the spin-plasmon momentum. Excitons appear on the surface when the gap in the surface spectrum is magnetically induced. Excitons correspond to the set of subgap levels with unusual dependence of the energy on orbital angular momentum quantum number and can be called 'chiral'. Contrary to conventional excitons chiral ones resonantly contribute to Hall component of optical conductivity tensor and play significant role in magneto-optical Faraday and Kerr effects. They resonantly enhance Faraday effect and reduce Kerr effect.

[en] Electron-hole pairing due to the Coulomb interaction in the system of two graphene sheets has been considered. The critical transition temperature has been determined as a function of both the distance between the electron and hole Fermi lines and the triangular distortion of their spectrum. It has been shown that when the distance between Fermi lines is longer than a critical value, the temperature of the transition to a state with nonzero momentum of Cooper pairs (Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state) is higher than the temperature of the transition to the Bardeen-Cooper-Schrieffer state. The Josephson effect for the FFLO state has been analyzed, which is due to the tunneling of charge carriers between the graphene sheets. It has been shown that the spatial structure of the order parameter of the system in this state can be reconstructed, i.e., the FFLO state can be identified from the dependence of the tunneling current on the magnetic field parallel to the graphene sheets. Other experimental methods for studying the phase diagram of the system have been discussed.

[en] Influence of Cooper pair fluctuations that are precursor of pairing of electrons and holes located on opposite surfaces of topological insulator film on tunnel conductivity between the surfaces is investigated. Due to restrictions caused by momentum and energy conservation dependence of tunnel conductivity on external bias voltage has peak that becomes more prominent with decreasing of disorder and temperature. We have shown that Cooper pair fluctuations considerably enhance tunneling and height of the peak diverges in vicinity of critical temperature with critical index ν = 2. Width of the peak tends to zero in proximity of critical temperature. Pairing of electrons and holes can be suppressed by disorder and in vicinity of quantum critical point height of the peak also diverges as function of Cooper pair damping with critical index μ = 2.

[en] One studies the superfluid features of a two-dimensional polariton system in an optical cavity. On the basis of the expression derivation for the effective low-energy action for the phase thermodynamic fluctuations one managed to obtain an expression for an analog of a superfluid density within the system in the current-current correlation function terms, and an expression for a current operator. One describes the Bogoliubov approximation for the polariton system and calculates the superfluid density. One discusses the Berezinski-Kosterlitz-Thouless transfer within the studied system

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