Abstract:
We study spectra of surface states in 2D topological insulators (TIs) based on HgTe/(Hg,Cd)Te quantum wells and 3D Bi$_2$Se$_3$-type compounds by constructing a class of feasible time-reversal invariant boundary conditions (BCs) for an effective ${\bf k}{\bf p}$-Hamiltonian and a tight-binding model of the topological insulators. The BCs contain some phenomenological parameters which implicitly depend on both bulk Hamiltonian parameters and crystal potential behavior near the crystal surface. Space symmetry reduces the number of the boundary parameters to four real parameters in the 2D case and three in the 3D case. We found that the boundary parameters may strongly affect not only an energy spectrum but even the very existence of these states inside the bulk gap near the Brillouin zone center. Nevertheless, we reveal in frames of the tight-binding model that when surface states do not exist in the bulk gap in the Brillouin zone center they cross the gap in other points of the Brillouin zone in agreement with the bulk-boundary correspondence.

Abstract:
The edge states which were observed on a linear edge of graphene may also persist on a curved edge. We calculate the elastic transport scattering cross section on a graphene nanohole supporting the edge states. Resonant peaks in the gate voltage dependence of conductivity of graphene with such nanoholes are obtained. Position and height of the resonances are determined by the localization depth of the quasibound edge states, and width -- by their lifetime. The scattering amplitude near the resonant energies has a strong valley asymmetry. We evaluate the effect of moderate edge rippling, inhomogeneity of boundary parameter along the edge, and Coulomb effects (charged nanohole) on the edge states and show that they do not affect the presence of the resonances, but can substantially influence their position, height and width. The local density of states near the nanohole also demonstrates a resonant dependence on gate voltage.

Abstract:
Graphene is a stable single atomic layer material exhibiting two-dimensional electron gas of massless Dirac fermions of high mobility. One of the intriguing properties of graphene is a possibility of realization of the Tamm-type edge states. These states differ from the usual surface states caused by defects, impurities and other imperfections at the edge of the system, as well as they differ from the magnetic edge states caused by skipping cyclotron orbits. The Tamm states result from breaking of periodic crystal potential at the edge, they can exist even at zero magnetic field and form a conducting band. Until recently those states have been observed in graphene only by local STM technique and there were no direct experiments on their contribution to transport measurements. Here we present the experiments on Aharonov-Bohm (AB) oscillations of resistance in a single-nanohole graphite and graphene structures, it indicates the presence of conducting edge states cycling around nanohole. An estimation show the penetration depth of the edge states to be as short as about 2 nm. The oscillations persist up to temperature T=115 K and the T-range of their existence increases with a decrease of the nanohole diameter. The proposed mechanism of the AB oscillations based on the resonant intervalley backscattering of the Dirac fermions by the nanohole via the Tamm states. The experimental results are consistent with such a scenario. Our findings show a way towards interference devices operating at high temperatures on the edge states in graphene

Abstract:
There are two types of intrinsic surface states in solids. The first type is formed on the surface of topological insulators. Recently, transport of massless Dirac fermions in the band of "topological" states has been demonstrated. States of the second type were predicted by Tamm and Shockley long ago. They do not have a topological background and are therefore strongly dependent on the properties of the surface. We study the problem of the conductivity of Tamm-Shockley edge states through direct transport experiments. Aharonov-Bohm magneto-oscillations of resistance are found on graphene samples that contain a single nanohole. The effect is explained by the conductivity of the massless Dirac fermions in the edge states cycling around the nanohole. The results demonstrate the deep connection between topological and non-topological edge states in 2D systems of massless Dirac fermions.

Abstract:
The dependence of the electric resistance R of nanoperforated graphene samples on the position of the Fermi level, which is varied by the gate voltage Vg, has been studied. Nanoperforation has been performed by irradiating graphene samples on a Si/SiO$_2$ substrate by heavy (xenon) or light (helium) ions. A series of regular peaks have been revealed on the R(Vg) dependence at low temperatures in zero magnetic field. These peaks are attributed to the passage of the Fermi level through an equidistant ladder of levels formed by orbitally quantized states of edge Dirac fermions rotating around each nanohole. The results are in agreement with the theory of edge states for massless Dirac fermions.

The results of the direct numerical integration
of the Navier-Stokes equations are evaluated against experimental data for problem
on a flow around bluff bodies in an unstable regime. Experiment records several
stable medium states for flow past a body. Evolution of each of these states, after
losing the stability, inevitably goes by periodic vortex shedding modes. Calculations
based on the Navier-Stokes equations satisfactorily reproduced all observed stable
medium states. They were, however, incapable of reproducing any of a vortex shedding
modes recorded experimentally. The solutions to the classic hydrodynamics equations
successfully reach the boundary of instability field. However, classic solutions
are unable to cross this boundary. Most likely, the reason for this is the Navier-Stokes
equations themselves. The classic hydrodynamics equations directly follow from the
Boltzmann equation and naturally contain the error involved in the derivation of
classic kinetic equation. Justthe Boltzmann
hypothesis, which closed kinetic equation, allowed us to con- struct classic hydrodynamics on only three lower
principal hydrodynamic values. The use of the Boltzmann hypothesis excludes higher
principal hydrodynamic values from the participation in the formation of classic
hydrodynamics equations. The multimoment hydrodynamics
equations are constructed using seven lower principal hydrodynamic values. The numerical
integration of the multimoment hydrodynamics equations in the problem on flow around
a sphere shows that the solutions to these equations cross the boundary and enter
the instability field. The boundary crossing is accompanied by appearance of very uncommon acts in scenario of system
evolution.

This work shows the results of a streamer discharge mode studies in various gas detectors developed up-to-date. The results are based on a new experimental data from high-speed thin-gap gas detector application developments as well as on basic knowledge of multi-wire devices operations.

Large numbers of precision fusion excitation functions were fitted in the literature using the nucleus-nucleus interaction potential having the Woods-Saxon shape. The diffuseness of this potential fusion ranges from 0.75 to 1.5 fm. This is much larger than the value of 0.65 fm required by the elastic scattering data. Trying to resolve this contradiction we develop the dissipative trajectory model based on the density-dependent M3Y NN-forces folded with the nuclear matter distribution. Resulting potential possesses the normal diffuseness about 0.65 fm. With this potential we reach the agreement with the data for ^{16}O+^{20}8Pb, ^{28}Si+^{208}Pb, ^{32}S+^{208}Pb reactions within 5%.

In the paper, we report about the possibilities to apply the photon sieve principle to binary diffractive lens in millimeter wave band. The FDTD simulation showing the idea of the photon sieve application to millimeter wave optics does not allow increasing the resolution power. The reason is the small number of holes in the FZP aperture. But such simulation results may be used as computational experiments of simple scale in millimeter wave allowing obtaining insight into physical systems which are characterized by nanometric objects, because the D/f and D/λ are almost the same.

It has been shown by thermodynamic and electro-chemical methods that coordination interactions are involved in the process of incorporation of rare-earth elements and/or Fe into Langmuir monolayers of oligomer with alkyl fragment. A coordination mechanism, which is responsible for self-organization of octahedral Fe(II)-complexes of nano-cyclic ligands obtained from oligomer of thiophene pyrrole series derivatives in compressed Langmuir monolayers has been proposed. It has been established that a coordinational-polymeric hexagonal network of nano-cyclic ligands with metal centers is formed at the phase transition when compressing the Langmuir monolayers of thiophene pyrrole series oligomer with alkyl fragment on surface of subphase with rare-earth (Sm, Er, Ce) and/or Fe ions.