Топологическая сверхпроводимость и майорановские состояния в низкоразмерных системах
The review discusses properties of superconducting phases with a nontrivial topology and conditions for their implementation in condensed matter, criteria for the appearance of the Majorana-type elementary excitations in solids, as well as principles and experimental methods for identifying Majorana bound states (MBSs). Along with the well-known models of the Kitaev chain and superconducting nanowire (SW) with spin-orbit interaction in an external magnetic ﬁeld, models of quasi-two-dimensional materials in which MBSs are realized in the presence of noncollinear spin ordering are considered. For the ﬁnite-length SW, a cascade of quantum transitions with a magnetic-ﬁeld change is demonstrated, accompanied by a change in the fermionic parity of the ground state. The anomalous behavior of the magnetocaloric eﬀect that occurs in this case can be used to probe MBSs. Considerable attention is paid to the analysis of transport characteristics of devices containing materials with non-trivial topology. The results of studying the conductance of Aharonov-Bohm ring that arms are connected by the SW are presented in detail. An important feature of this device is the appearance of Fano resonances in the magnetic-ﬁeld dependence of the conductance when the SW is in the topologically nontrivial phase. A relationship has been established between the characteristics of such resonances and the spatial structure of the SW state with the lowest energy. Within the framework of the t-J-V model on a triangular lattice, the conditions for the MBS appearance in the phase of coexistence of chiral d + id superconductivity and 120-degree spin ordering are determined. When electron-electron interactions are taken into account, topological invariants of low-dimensional superconducting materials with noncollinear spin ordering are considered. The formation of Majorana modes in regions with an odd value of the topological Z-invariant is demonstrated. The spatial structure of these excitations in the ensemble of Hubbard fermions is determined.