We discuss the properties of topologically nontrivial superconducting phases and the conditions for their realization in condensed matter, 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 (SW) 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 SWs, 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 conductance of an Aharonov–Bohm ring whose arms are connected by an SW 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 SW is in a topologically nontrivial phase. We establish a relation between the characteristics of such resonances and the spatial structure of the lowest-energy SW 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.

中文翻译：

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低维系统中的拓扑超导性和马约拉纳态

我们讨论了拓扑非平凡超导相的性质及其在凝聚态物质中实现的条件，固体中基本马约拉纳型激发的出现标准，以及识别马约拉纳束缚态（MBS）的相应原理和实验方法。除了著名的基塔耶夫链和在外部磁场中具有自旋轨道耦合的超导纳米线 (SW) 模型之外，我们还讨论了准二维材料模型，其中在非共线自旋排序的情况下实现了 MBS。对于有限长度的SW，我们证明了随着磁场变化而发生的一系列量子跃迁，并伴随着基态费米子宇称的变化。磁热效应的相应异常行为可以用作识别 MBS 的工具。我们非常重视对包含拓扑非平凡材料的器件的传输特性的分析。详细讨论了通过 SW 连接臂的阿哈罗诺夫-玻姆环的电导研究结果。该装置的一个重要特征是，当 SW 处于拓扑非平凡相时，电导对磁场的依赖性会出现法诺共振。我们建立了这种共振的特征与最低能量 SW 态的空间结构之间的关系。手性 d+id 超导性和 120 度自旋有序共存相中 MBS 的发生条件是在三角晶格上的 t-J-V 模型框架内确定的。我们在讨论具有非共线自旋排序的低维超导材料的拓扑不变量时考虑了电子-电子相互作用。证明了在具有奇数拓扑 ℤ 不变量值的区域中马约拉纳模的形成。哈伯德费米子系综中这些激发的空间结构被确定。