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Information is presented on the state of research on the effect of hydrogen on the superconducting properties of various compounds. The review consists of an introduction, one appendix and four sections: methods for the synthesis of modern hydrogen-containing superconductors, experimental studies of the properties of hydrogen-containing superconductors, on the mechanisms of the influence of hydrogen on superconductivity, problems and prospects of hydrogen-containing superconductors., Comment: 108 pages, 77 figures

We study the magnon spectrum in skyrmion crystal formed in thin ferromagnetic films with Dzyalosinskii-Moria interaction in presence of magnetic field. Focusing on two low-lying observable magnon modes and employing stereographic projection method, we develop a theory demonstrating a topological transition in the spectrum. Upon the increase of magnetic field, the gap between two magnon bands closes, with the ensuing change in the topological character of both bands. This phenomenon of gap closing, if confirmed in magnetic resonance experiments, may deserve further investigation by thermal Hall conductivity experiments., Comment: 6 pages, 4 figures

We discuss the Goldstone mode of skyrmion crystal in a model of two-dimenssional ferromagnet with Dzyaloshinskii-Moriya interaction in magnetic field. We use stereographic projection approach to construct skyrmion crystal and consider skyrmion's displacement field. The small overlap of the individual skyrmion images restricts the potential energy to the interaction of nearest neighboring displacements. The closed form of the Goldstone mode dispersion is found and its dependence on the magnetic field is studied. We use semiclassical quantization to define the Green's function and show that the propagation of displacements through the crystal changes its tensorial form from isotropic to anisotropic one at large distances., Comment: 6 pages, 4 figures

Using stereographic projection approach we develop a theory for calculation of dynamical susceptibility tensor of Skyrmion crystals (SkX), formed in thin ferromagnetic films with Dzyaloshinskii-Moriya interaction and in the external magnetic field. Staying whenever possible within analytical framework, we employ the model anzats for static SkX configuration and discuss small fluctuations around it. The obtained formulas are numerically analyzed in the important case of uniform susceptibility, accessible in magnetic resonance (MR) experiments. We show that, in addition to three characteristic MR frequencies discussed earlier both theoretically and experimentally, one should also expect several resonances of smaller amplitude at somewhat higher frequencies.

Using semiclassical method combined with stereographic projection approach, we investigate the magnetic dynamics of the skyrmion crystal (SkX), formed in planar ferromagnet with both Dzyaloshinskii-Moriya interaction and uniform magnetic field. The topologically non-trivial ground state of SkX is described in stereographic projection by the complex valued function with simple poles at skyrmions' positions. We use the earlier proposed ansatz for this ground state function in the form of the sum of individual skyrmions. The dynamics follows from the second variation of the classical action. Numerical analysis yields the magnon band structure of tight-binding form in accordance with previously known results. There are two sets of bands, one set with a flat dispersion, topologically trivial and rapidly evolving with magnetic field. Another set is robust to magnetic field, characterized by pronounced dispersion and with the Berry curvature which may be sign-reversal in the Brillouin zone. The developed theory can be straightforwardly generalized for the analysis of magnetic dynamics in topological spin structures of other types.

As a result of experimental studies of the single-crystal iron-chalcogenide compound FeTe0.65Se0.35, the effect of structural transitions caused by hydrogen sorption on the magnetic and current-carrying properties of a superconductor has been established. An increase in the volume-averaged effective pinning potential (and the associated critical current density) after the process of hydrogen sorption at temperatures up to 150 {\deg}C - 200 {\deg}C can be explained by the appearance of additional pinning centers due to the local action of implanted H ions on its crystal structure and electronic states. It was confirmed that hydrogenation is an efficient tool for increasing flux pining properties of superconductors.

It is commonly assumed that a lattice of skyrmions, emerging in two-dimensional non-centrosymmetric magnets in external magnetic fields, can be represented as a sum of three magnetic helices. In order to test this assumption we compare two approaches to a description of regular skyrmion structure. We construct (i) a lattice of Belavin-Polyakov-like skyrmions within the stereographic projection method, and (ii) a deformed triple helix defined with the use of elliptic functions. The estimates for the energy density and magnetic profiles show that these two ansatzes are nearly identical at zero temperature for intermediate magnetic fields. However at higher magnetic fields, near the transition to topologically trivial uniform phase, the stereographic projection method is preferable, particularly, for the description of disordered skyrmion liquid phase. We suggest to explore the intensities of the secondary Bragg peaks to obtain the additional information about the magnetic profile of individual skyrmions. We estimate these intensities to be several percents of the main Bragg peak at high magnetic fields.

We consider multiskyrmion configurations in 2D ferromagnets with Dzyaloshinskii-Moriya (DM) interaction and the magnetic field, using the stereographic projection method. In the absence of DM interaction, $D$, and the field, $B$, the skyrmions do not interact and the exact multiskyrmion solution is a sum of individual projections. In certain range of $B, D\neq0$, skyrmions become stable and form a hexagonal lattice. The shape of one skyrmion on the plane is fully determined by $D$ and $B$. We describe multiskyrmion configurations by simple sums of individual skyrmion projections, of the same shape and adjusted scale. This procedure reveals pairwise and triple interactions between skyrmions, and the energy of proposed hexagonal structure is found in a good agreement with previous studies. It allows an effective theory of skyrmion structures in terms of variables, referring to individual skyrmions, i.e., their position, size and phase, elliptic distortions etc., Comment: 5 pages, 4 figures

The magnetic moment in the superconducting and normal state of a crystalline FeTe0.65Se0.35 superconductor, grown by the Bridgman's method with relatively high growth rate, was measured. The temperature and magnetic field dependences of magnetization and its relaxation time were determined. Studied crystal, being non-uniform due to high growth rate of 5 mm/h, exhibits smaller width of superconducting transition in comparison with an ideal crystal grown with velocity of 1 mm/h, and the difference in magnetic properties of crystals grown with various growth rate, related to their microstructure, is discussed., Comment: 9 pages, 6 figures

The issue concerning the nature and the role of microstructural inhomogeneities in iron chalcogenide superconducting crystals of FeTe0.65Se0.35 and their correlation with transport properties of this system was addressed. Presented data demonstrate that chemical disorder originating from the kinetics of the crystal growth process significantly influences the superconducting properties of an Fe-Te-Se system. Transport measurements of the transition temperature and critical current density performed for microscopic bridges allow us to deduce the local properties of a superconductor with microstructural inhomogeneities, and significant differences were noted. The variances observed in the local properties were explained as a consequence of weak superconducting links existing in the studied crystals. The results confirm that inhomogeneous spatial distribution of ions and small hexagonal symmetry nanoscale regions with nanoscale phase separation also seem to enhance the superconductivity in this system with respect to the values of the critical current density. Magnetic measurements confirm the conclusions drawn from the transport measurements., Comment: 20 pages, 5 figures