论文标题
经受磁通量的拓扑超导体的通用相图
Universal phase diagram of topological superconductors subjected to magnetic flux
论文作者
论文摘要
我们对磁场对$ p_ {x}+ip_ {y} $拓扑超导体的接近耦合岛阵列的轨道效应进行了理论研究。为了描述系统，我们将霍夫斯塔特蝴蝶的紧密结合模型推广到包括超导岛的效果。在没有超导性的情况下出现的量子厅拓扑阶段的特征是整数费尔米奇的chern数量，对应于被占领的散装兰道水平的数量。随着超导配对的强度增加了一系列过渡，每个连续阶段的手性majorana边缘模式较小，从而导致费米尼克·克恩（Fermionic Chern）的数量减少了一半。当配对势超过紧密结合模型带宽时，库珀对位于岛屿中，Chern数为零，并且没有低能的边缘模式。我们在模型的参数空间中识别系统是拓扑的域，并支持奇数的手性Majorana边缘模式。尽管域的精确形状取决于模型的细节，但相图的一般结构是可靠的，并且在数值上和几种简化的可追溯分析模型中获得。我们讨论了这项研究与半导体系统上二维超导体阵列的最新实验研究的相关性。
We perform a theoretical study of the orbital effect of a magnetic field on a proximity-coupled islands array of $p_{x}+ip_{y}$ topological superconductors. To describe the system, we generalize the tight-binding model of the Hofstadter butterfly to include the effect of the superconducting islands. The quantum Hall topological phases, appearing in the absence of superconductivity, are characterized by integer fermionic Chern numbers corresponding to the number of occupied bulk Landau levels. As the strength of the superconducting pairing increases a series of transitions occurs, with one less chiral Majorana edge mode at each consecutive phase, leading to a reduction of the fermionic Chern number by a half. When the pairing potential exceeds the tight-binding model bandwidth, Cooper pairs are localized in the islands, the Chern number is zero, and there are no low-energy edge modes. We identify domains in the model's parameter space for which the system is topological and supports an odd number of chiral Majorana edge modes. While the precise shape of the domains depends on the details of the model, the general structure of the phase diagram is robust, and it is obtained numerically and in several simplified traceable analytical models. We discuss the relevance of this study to recent experimental research of two-dimensional superconductor arrays on semiconductor systems.
