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## Low-temperature Hall effect in bismuth chalcogenides thin films

Bismuth chalcogenides are the most studied 3D topological insulators. As a rule, at low temperatures, thin films of these materials demonstrate positive magnetoresistance due to weak antilocalization. Weak antilocalization should lead to resistivity decrease at low temperatures; in experiments, however, resistivity grows as temperature decreases. From transport measurements for several thin films ( with various carrier density, thickness, and carrier mobility), and by using a purely phenomenological approach, with no microscopic theory, we show that the low-temperature growth of the resistivity is accompanied by growth of the Hall coefficient, in agreement with the diffusive electron-electron interaction correction mechanism. Our data reasonably explain the low-temperature resistivity upturn.

We analyze the entanglement spectrum of superfluid phases of $^3$He, the 3D B-phase and the planar phase in two dimensions. We find explicitly the wave functions of the low-lying eigenstates, including Majorana zero modes, as well as the corresponding part of the spectrum of the entanglement Hamiltonian.

Collective plasmon excitations in a helical electron liquid on the surface of strong three-dimensional topological insulator are considered. The properties and internal structure of these excitations are studied. Due to spin-momentum locking in helical liquid on a surface of topological insulator, the collective excitations should manifest themselves as coupled charge- and spin-density waves.

We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current and the critical radius of the ring beyond which this current gets exponentially suppressed by quantum fluctuations. We also analyze fluctuations of persistent current caused by quantum phase slips. At low temperatures the supercurrent noise spectrum has the form of coherent peaks which can be tuned by the magnetic flux. Experimental observation of these peaks can directly demonstrate the existence of plasma modes in superconducting nanorings.

International Conference \Advanced Element Base of Micro- and Nano-Electronics with Using To-date Achievements of Theoretical Physics" is an annual conference of Faculty for Physics and Mathematics of Moscow Region State University (MRSU). MRSU is a leading Russian regional university. This conference is traditionally organized by Department of Theoretical Physics. The conference attracted around 120 participants from many countries and Russian regions. They have applied 83 papers to a special JPCS issue. Special session was devoted to RD of graduate and post-graduate students. The Conference program included sessions as follows:

To-Date Theoretical Physics Problems Electronics Technologies and Materials Condensed Matter Physics Aerohydrodynamics Plasma Physics Electronic devices for biological applications Space Physics and Technologies Education of Physics, Electronics and Information TechnologiesBesides of oral talks at typical scienti c sessions many papers are to be presented on-line with using to-date communication facilities. Therefore, many participants from oversea countries and Russian regions have a good opportunity to tell about their recent RD results and discuss to-date scienti c problems. Many famous scienti c organizations applied their participation in the Conference: Institute of Solid State Physics of Russian Academy of Sciences (RAS), Steklov Mathematics Institute of RAS, Moscow Institute of Physics and Technology (Technical University), Lomonosov Moscow State University, Federal RD Center of RAS \Crystallography and Photonics", Saint-Petersburg State University, Kurchatov Institute, Alikhanov Institute of Theoretical and Applied Physics, Keldysh Institute of Applied Mathematics of RAS, Computational Center of RAS, RUDN University, Bauman Moscow State Technology University, Donghua University (Shanghai, China), Higher School of Economics - National Research University, Moscow Aviation Institute (Technology University), JSC Cyclon, JSC Pulsar, BOE (China, Russian Oce), Northern Federal University (Arkhangelsk), Demidov Yaroslavl State University, Saratov National Research State University named after N. G. Chernyshevsky, Moscow Regional Research and Clinical Institute "MONIKI", K.G. Razumovsky Moscow State University of Technologies and Management (the First Cossack University), Moscow State University of Design and Technology and many others.

A big group of master, bachelor and post-graduate students from Institute of Solid State Physics of RAS, MRSU, MIPT, RUDN University presented their research results. The International Conference \Advanced Element Base of Micro- and Nano-Electronics with Using To-date Achievements of Theoretical Physics" becomes very important scienti c event with signi cant results of big importance for basic science and practical application.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.