We discuss the properties of topologically nontrivial superconducting phases and the conditions for their realization in condensed media, the criteria for the appearance of elementary Majorana-type excitations in solids, and the corresponding principles and experimental methods for identifying Majorana bound states (MBSs). Along with the well-known Kitaev chain and superconducting nanowire (SNW) models with spin--orbit coupling in an external magnetic field, we discuss models of quasi-two-dimensional materials in which MBSs are realized in the presence of noncollinear spin ordering. For finite-length SNWs, we demonstrate a cascade of quantum transitions occurring with a change in the magnetic field, accompanied by a change in the fermion parity of the ground state. The corresponding anomalous behavior of the magnetocaloric effect can be used as a tool for identifying MBSs. We devote considerable attention to the analysis of the transport characteristics of devices that contain topologically nontrivial materials. The results of studying the conductivity of an Aharonov--Bohm ring whose arms are connected by an SNW are discussed in detail. An important feature of this device is the appearance of Fano resonances in the dependence of conductance on the magnetic field when the SNW is in a topologically nontrivial phase. We establish a relation between the characteristics of such resonances and the spatial structure of the lowest-energy SNW state. The conditions for the occurrence of an MBS in the phase of the coexistence of chiral d+id superconductivity and 120-degree spin ordering are determined in the framework of the t-J-V model on a triangular lattice. We take electron--electron interactions into account in discussing the topological invariants of low-dimensional superconducting materials with noncollinear spin ordering. The formation of Majorana modes in regions with an odd value of a topological ℤ invariant is demonstrated. The spatial structure of these excitations in the Hubbard fermion ensemble is determined.

Keywords: low-dimensional system, Majorana bound state, spin—orbit coupling, topological invariant, Coulomb correlations, noncollinear magnetism, topological superconductivity, quantum transport PACS: 71.20.Nr, 71.20.Ps, 71.23.An, 71.70.Ej, 73.23.−b, 74.20.Rp, 74.25.F−, 74.90.+n (all) DOI: 10.3367/UFNe.2021.03.038950 URL: https://ufn.ru/en/articles/2022/1/b/ 000788597000002 2-s2.0-85127103681 2022PhyU...65....2V Citation: Val’kov V V, Shustin M S, Aksenov S V, Zlotnikov A O, Fedoseev A D, Mitskan V A, Kagan M Yu "Topological superconductivity and Majorana states in low-dimensional systems" Phys. Usp. 65 2–39 (2022) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 26th, May 2020, revised: 18th, December 2020, accepted: 11th, March 2021 Оригинал: Вальков В В, Шустин М С, Аксенов С В, Злотников А О, Федосеев А Д, Мицкан В А, Каган М Ю «Топологическая сверхпроводимость и майорановские состояния в низкоразмерных системах» УФН 192 3–44 (2022); DOI: 10.3367/UFNr.2021.03.038950