Zou Jinyu, Xie Qing, Song Zhida, Xu Gang
Wuhan National High Magnetic Field Center & School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.
Department of Physics, Princeton University, Princeton, NJ 08544, USA.
Natl Sci Rev. 2020 Jul 24;8(5):nwaa169. doi: 10.1093/nsr/nwaa169. eCollection 2021 May.
We classify gapped topological superconducting (TSC) phases of one-dimensional quantum wires with local magnetic symmetries, in which the time-reversal symmetry [Formula: see text] is broken, but its combinations with certain crystalline symmetries, such as [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], are preserved. Our results demonstrate that an equivalent BDI class TSC can be realized in the [Formula: see text] or [Formula: see text] superconducting wire, which is characterized by a chiral invariant. More interestingly, we also find two types of totally new TSC phases in the [Formula: see text] and [Formula: see text] superinducting wires, which are beyond the known AZ class, and are characterized by a helical invariant and ⊕ invariants, respectively. In the TSC phase, pairs of Majorana zero modes (MZMs) are protected at each end. In the [Formula: see text] case, the MZMs can be either chiral or helical, and even helical-chiral coexisting. The minimal models preserving [Formula: see text] or [Formula: see text] symmetry are presented to illustrate their novel TSC properties and MZMs.
我们对具有局域磁对称性的一维量子线的带隙拓扑超导（TSC）相进行了分类，其中时间反演对称性[公式：见正文]被打破，但其与某些晶体对称性的组合，如[公式：见正文]、[公式：见正文]、[公式：见正文]和[公式：见正文]得以保留。我们的结果表明，等效的BDI类TSC可以在[公式：见正文]或[公式：见正文]超导导线中实现，其特征是一个手征不变量。更有趣的是，我们还在[公式：见正文]和[公式：见正文]超导导线中发现了两种全新的TSC相，它们超出了已知的AZ类，分别以螺旋不变量和[公式：见正文]⊕不变量为特征。在[公式：见正文]TSC相中，每一端都有一对马约拉纳零模（MZMs）受到保护。在[公式：见正文]的情况下，MZMs可以是手征的或螺旋的，甚至是螺旋 - 手征共存的。给出了保持[公式：见正文]或[公式：见正文]对称性的最小模型，以说明它们新颖的TSC性质和MZMs。
