超导纳米线拓扑邻近效应的准经典Eilenberger理论
Quasiclassical Eilenberger theory of the topological proximity effect in a superconducting nanowire
摘要：
利用准经典Eilenberger理论研究了具有p波序参量的纳米线与金属纳米线之间的拓扑超导邻近效应。该模型忠实地代表了实验装置的关键定性特征，其中只有一部分纳米线与块状超导体直接接触，诱导拓扑超导性。它表明，Eilenberger方程代表了一个可行的替代Bogoliubov-de Gennes理论的拓扑超导异质结构，并提供了一个更简单的定量描述的一些观测。对于我们的设置，我们获得了准经典格林函数和态密度作为位置和能量的函数的精确解析解。由边界引起的相关性涉及与p波和奇频配对相关的项，这些项相互交织，并对平等的基础上的可观测性做出贡献。我们恢复签名的标准马约拉纳模式的超导段的末端附近，但没有发现这样的本地化模式中诱导的金属段。相反，零偏置功能是分散在整个金属部分根据以前的作品。在较短的电线，马约拉纳模式和离域峰分裂远离零能量。对于长金属段，非拓扑Andreev束缚态出现并最终合并在一起，产生无带隙超导体。
英文摘要：
We use the quasiclassical Eilenberger theory to study the topological superconducting proximity effects between a segment of a nanowire with a p-wave order parameter and a metallic segment. This model faithfully represents key qualitative features of an experimental setup, where only a part of a nanowire is in immediate contact with a bulk superconductor, inducing topological superconductivity. It is shown that the Eilenberger equations represent a viable alternative to the Bogoliubov-de Gennes theory of the topological superconducting heterostructures and provide a much simpler quantitative description of some observables. For our setup, we obtain exact analytical solutions for the quasiclassical Green's functions and the density of states as a function of position and energy. The correlations induced by the boundary involve terms associated with both p-wave and odd-frequency pairing, which are intertwined and contribute to observables on an equal footing. We recover the signatures of the standard Majorana mode near the end of the superconducting segment, but find no such localized mode induced in the metallic segment. Instead, the zero-bias feature is spread out across the entire metallic part in accordance with the previous works. In shorter wires, the Majorana mode and delocalized peak split up away from zero energy. For long metallic segments, non-topological Andreev bound states appear and eventually merge together, giving rise to a gapless superconductor.
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