论文标题

使用扰动访问耦合超导平台中的不同拓扑类别和类型的Majorana边缘状态

Accessing different topological classes and types of Majorana edge states in coupled superconducting platforms using perturbations

论文作者

Ray, Sayonee, Mukerjee, Subroto, Shah, Nayana

论文摘要

对拓扑类别及其相关边缘状态的研究一直具有持续的兴趣。在一个维度上,这些研究的标准平台是常规的基塔夫电线及其实现。在这项工作中,我们在实验相关的扰动的情况下(如Zeeman Field和S-Wave SC)研究了1D耦合P-波平台的边缘状态。首先,我们表明,根据有效现场电位的价值,不受干扰的耦合p波设置可以具有两种类型的Majorana边缘状态。我们表明,诸如Zeeman字段和S波术语之类的其他组件可能会导致向不同的对称类别的过渡,无论是拓扑琐碎还是不乏味,并改变了这些边缘状态的性质。在存在扰动的情况下,我们表明当有效的P波配对在自旋物种之间等于2时,当两者之间的配对差异在两者之间的相差时,有3个对称类别。其中一些类别在拓扑上是非平凡的。此外,当我们在两个这样的拓扑设置及其相应的行为与p波阶参数的阶段之间有一个连接时,我们探讨了子段状态的性质。我们的工作提供了一种理论框架,该框架使用实验可行的扰动,在耦合的P-Wave纳米线设置中获得非平凡的拓扑类别,以及在这些平台的连接范围内的子段状态的性质。

The study of topological classes and their associated edge states has been of ongoing interest. In one dimension, the standard platform of these studies has been the conventional Kitaev wire and its realizations. In this work, we study the edge states in coupled p-wave platforms in 1D, in the presence of experimentally relevant perturbations, like a Zeeman field and s-wave SC. Firstly, we show that the unperturbed coupled p-wave setup by itself can have two types of Majorana edge states, depending on the value of the effective onsite potential. We show that additional components like Zeeman field and s-wave term can cause transitions to different symmetry classes, both topologically trivial or non-trivial, and change the nature of these edge states. In the presence of the perturbations, we show that there are 3 symmetry classes when the effective p-wave pairing is equal between the spin species, and 6 for the second kind, when the pairing differs by a phase $π$ between the two. Some of these classes are topologically non-trivial. Further, we explore the nature of subgap states when we have a junction between two such topological setups and their corresponding behaviour with the phase of the p-wave order parameter. Our work provides a theoretical framework of the different ways to get non-trivial topological classes in coupled p-wave nanowire setup, using experimentally feasible perturbations, and the nature of subgap states across junctions of these platforms.

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