Department of Physics, Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), Beihang University, Beijing, 100191, China.
Beijing Computational Science Research Center, Beijing, 100089, China.
Sci Rep. 2017 Aug 23;7(1):9210. doi: 10.1038/s41598-017-09160-x.
By analogy to the topological models of fermions in one-dimensional periodically modulated lattices, we provide a systematic method to construct topological superconductors in BDI class. We then create superlattices of Majorana fermions to interpolate several Majorana chains, and realize topological superconductors with arbitrary winding numbers. Two kinds of chiral symmetries are identified in the systems with multiple chains. Of the two winding numbers associated to the chiral symmetries, one counts the number of zero-energy modes, while the other counts the difference of the numbers of α- and β-type Majorana zero states. We also show that one α- and one β-type Majorana zero modes collapse into fractional charged zero states when they are spatially intertwined. In the systems with odd number of chains, it induces topological superconductors with coexistence of fractional charged zero states and Majorana zero states. Finally by introducing symmetry breaking term, we present an intuitive explanation of the Z nature of the topological invariant in the D class.
我们类比了在一维周期性调制晶格中费米子的拓扑模型，提供了一种系统的方法来构造 BDI 类中的拓扑超导体。然后，我们创建了马约拉纳费米子的超晶格来插值几个马约拉纳链，并实现了具有任意缠绕数的拓扑超导体。在具有多个链的系统中，我们确定了两种手征对称性。与手征对称性相关的两个缠绕数中，一个数是零能模的数量，另一个数是α型和β型马约拉纳零态数量的差值。我们还表明，当两个α型和β型马约拉纳零模在空间上相互缠绕时，它们会坍缩为分数电荷零态。在具有奇数个链的系统中，它会诱导具有分数电荷零态和马约拉纳零态共存的拓扑超导体。最后，通过引入对称破缺项，我们对 D 类拓扑不变量的 Z 性质给出了直观的解释。
