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## Anomalous Josephson Current via Majorana Bound States in Topological Insulators

We propose a setup involving Majorana bound states (MBS) hosted by a vortex on a superconducting surface of a 3D topological insulator (TI). We consider a narrow channel drilled across a TI slab with both sides covered by

In order to model the processes taking place in systems with Josephson contacts, a differential equation on a torus with three parameters is used. One of the parameters of the system can be considered small and the methods of the fast-slow systems theory can be applied. The properties of the phase-lock areas – the subsets in the parameter space, in which the changing of a current doesn’t affect the voltage — are important in practical applications. The phaselock areas coincide with the Arnold tongues of a Poincare map along the period. A description of the limit properties of Arnold tongues is given. It is shown that the parameter space is split into certain areas, where the tongues have different geometrical structures due to fastslow effects. An efficient algorithm for the calculation of tongue borders is elaborated. The statement concerning the asymptotic approximation of borders by Bessel functions is proven.

In order to model the processes taking place in systems with Josephson contacts, a differential equation on a torus with three parameters is used. One of the parameters of the system can be considered small and the methods of the fast-slow systems theory can be applied. The properties of the phase-lock areas – the subsets in the parameter space, in which the changing of a current doesn’t affect the voltage — are important in practical applications. The phaselock areas coincide with the Arnold tongues of a Poincare map along the period. A description of the limit properties of Arnold tongues is given. It is shown that the parameter space is split into certain areas, where the tongues have different geometrical structures due to fastslow effects. An efficient algorithm for the calculation of tongue borders is elaborated. The statement concerning the asymptotic approximation of borders by Bessel functions is proven.

A three-parametrical family of ODEs on a torus arises from a model of Josephson effect in a resistive case when a Josephson junction is biased by a sinusoidal microwave current. We study asymptotics of Arnold tongues of this family on the parametric plane (the third parameter is fixed) and prove that the boundaries of the tongues are asymptotically close to Bessel functions.

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.

By using superconducting quantum interference device (SQUID) magnetometry, we investigated anisotropic high-field (H less than or similar to 7T) low-temperature (10 K) magnetization response of inhomogeneous nanoisland FeNi films grown by rf sputtering deposition on Sitall (TiO2) glass substrates. In the grown FeNi films, the FeNi layer nominal thickness varied from 0.6 to 2.5 nm, across the percolation transition at the d(c) similar or equal to 1.8 nm. We discovered that, beyond conventional spin-magnetism of Fe21Ni79 permalloy, the extracted out-of-plane magnetization response of the nanoisland FeNi films is not saturated in the range of investigated magnetic fields and exhibits paramagnetic-like behavior. We found that the anomalous out-of-plane magnetization response exhibits an escalating slope with increase in the nominal film thickness from 0.6 to 1.1 nm, however, it decreases with further increase in the film thickness, and then practically vanishes on approaching the FeNi film percolation threshold. At the same time, the in-plane response demonstrates saturation behavior above 1.5-2T, competing with anomalously large diamagnetic-like response, which becomes pronounced at high magnetic fields. It is possible that the supported-metal interaction leads to the creation of a thin charge-transfer (CT) layer and a Schottky barrier at the FeNi film/Sitall (TiO2) interface. Then, in the system with nanoscale circular domains, the observed anomalous paramagnetic-like magnetization response can be associated with a large orbital moment of the localized electrons. In addition, the inhomogeneous nanoisland FeNi films can possess spontaneous ordering of toroidal moments, which can be either of orbital or spin origin. The system with toroidal inhomogeneity can lead to anomalously strong diamagnetic-like response. The observed magnetization response is determined by the interplay between the paramagnetic-and diamagnetic-like contributions.

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.