Abstract

Using the Bogoliubov–de Gennes Hamiltonian, we analytically study two models with superconducting order, the p-wave model with an impurity potential and the s-wave nanowire model with superconductivity induced by the proximity effect with an impurity potential in a Zeeman field with a spin–orbit interaction. Using the Dyson equation, we study conditions for the emergence of Andreev bound states with energies close to the boundary of the superconducting gap and the possibility for these states to pass into Majorana-like bound states. We prove that in the topological phase (in the p-wave case also in the trivial phase) for both models, the Andreev bound states with energy close to the boundary of the superconducting gap can exist, but although their emergence in the p-wave model is due to the appearance of a (nonmagnetic) impurity, they appear in the s-wave model only as a result of a local perturbation of the Zeeman field. For both models, the transition of the Andreev bound states into the Majorana states (and back) is impossible in the topological phase, which is explained by the topological protection of the Majorana-like bound states in the topological phase.

中文翻译：

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在超导间隙中安德列夫和马约拉那束缚态的相互过渡

摘要

使用Bogoliubov-de Gennes哈密顿量，我们分析了两个具有超导阶数的模型，一个是在杂散态的塞曼场中，一个具有杂质电势的p波模型和一个由具有杂质电势的邻近效应感应到的具有超导性的s波纳米线模型。自旋轨道相互作用。使用戴森方程，我们研究了能量接近超导间隙边界的安德列夫束缚态的出现条件，以及这些态进入马约拉那状束缚态的可能性。我们证明，在两个模型的拓扑阶段（在p波情况下，在平凡阶段也是如此），可以存在能量接近超导间隙边界的Andreev束缚态，但是尽管它们出现在p波中模型是由于（非磁性）杂质的出现，它们仅由于塞曼场的局部扰动而出现在s波模型中。对于这两种模型，在拓扑阶段都不可能将Andreev束缚态转换为Majorana态（和向后），这可以通过拓扑阶段中的Majorana类束缚态的拓扑保护来解释。