Abstract

We consider three one-dimensional superconducting structures: 1) the one with \(p\)-wave superconductivity; 2) the main experimental model of a nanowire with \(s\)-wave superconductivity generated by the bulk superconductor due to the proximity effect in an external magnetic field and Rashba spin–orbit interaction; 3) the boundary of a two-dimensional topological insulator with an \(s\)-wave superconducting order in an external magnetic field. We obtain precise analytic results for the “superconductor–magnetic impurity–superconductor” model. Using the Bogoliubov–de Gennes Hamiltonian, we study the behavior of stable states arising in these structures, with energies near the edges of the energy gap of “electron” (“hole ”) type for the first model and “electron plus hole” type for the other two models in the case where the system passes from the topological phase to the trivial one. For the topological phase transition, resonance (decaying ) states turn out to play a major role; the spin flip and the change of sign of the charge occur due to the transition of bound states to resonance ones and vice versa with their energy changing to the opposite ones as the gap closes. The results are consistent with the absence of a zero-bias conductance peak in the trivial topological phase observed in a recent experiment.

中文翻译：

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Andreev 态在拓扑相变中的行为

摘要

我们考虑三种一维超导结构：1）具有\(p\)-波超导性的结构；2)由于外部磁场中的邻近效应和 Rashba 自旋轨道相互作用，体超导体产生具有\(s\)波超导性的纳米线的主要实验模型；3) 具有\(s\)的二维拓扑绝缘体的边界外磁场中的波超导有序。我们获得了“超导体-磁性杂质-超导体”模型的精确解析结果。使用 Bogoliubov-de Gennes 哈密顿量，我们研究了这些结构中出现的稳定状态的行为，能量接近第一个模型的“电子”（“空穴”）型和“电子加空穴”型能隙边缘对于其他两个模型，在系统从拓扑阶段过渡到平凡阶段的情况下。对于拓扑相变，共振（衰减）状态起到了主要作用；自旋翻转和电荷符号的变化是由于束缚态向共振态的转变而发生的，反之亦然，随着间隙的关闭，它们的能量转变为相反的态。