Topological excitations in field theory models of superconductivity and magnetism

Abstract: Topological excitations are subjects of intensive studies in physics and mathematics. In solid-state and soft matter physics, topological excitations can largely determine the thermodynamic and electromagnetic properties of materials, while in high energy physics they were theorized as particles. The corresponding theories are based on field models, which are among the pillars of theoretical physics.Field theory models of superconductivity and magnetism are the theoretical basis for this work. Topological excitations in superconductors and magnets have been studied since the middle of the last century. Since then, a huge amount of work has been accumulated on vortices, Bloch points and skyrmions. In this popular topic, we discovered new phenomena. The main results are:Discovery and theory of skyrmion braids in cubic chiral magnets. Coexistence of type-I and type-II superconductivity signatures in muon spin rotation measurements on ZrB_{12} explained by theoretical modeling of vortex states giving qualitative agreement. Theory and experimental evidence of magnetic field controlled pairwise interaction of skyrmions in cubic chiral magnets. Experimental observation of chiral bobbers predicted in theory by Rybakov et al. (2015). Theory of a new type of magnetic ordering - antichiral ferromagnetism - giving rise to unique skyrmions.  Generalization of the Bogdanov-Yablonskii solution (1989) for classical models of magnets from the case of a skyrmion with a topological charge of -1 (+1) to the case of all integer charges. Positive answer to the Babaev-Faddeev-Niemi hypothesis (2002) on the existence of knot excitations in the superconducting state by demonstrating stable solutions in a model that takes into account the Andreev-Bashkin effect.