论文标题
部分可观测时空混沌系统的无模型预测
The $\mathbf{Z}_{2}$ topological invariants in 2D and 3D topological superconductors without time reversal symmetry
论文作者
论文摘要
在拓扑分类理论中，没有时间逆转对称性的2D拓扑超导体的特征是Chern数字。但是，实际上，我们发现Chern数字无法揭示拓扑超导体边界状态的全部特性。我们找出一些与Chern Numbers相比，一些相关的粒子孔对称性相关$ \ MATHBF {Z} _ {2} $不变式提供的拓扑超导体的其他信息。使用$ \ mathbf {z} _ {2} $不变，我们在2D系统中定义了弱而强的拓扑超导体。此外，我们解释了Chern数字与拓扑超导体中边界状态数量之间不匹配的原因，并声称强大的Majorana零模式的特征是$ \ Mathbf {Z} _ {2} _ varriant而不是Chern数字。我们还将$ \ mathbf {z} _ {2} $不变性扩展到3D非时代反转对称超导体系统，包括差距和无间隙情况。
In theory of topological classification, the 2D topological superconductors without time reversal symmetry are characterized by Chern numbers. However, in reality, we find the Chern numbers can not reveal the whole properties of the boundary states of the topological superconductors. We figure out some particle-hole symmetry related $\mathbf{Z}_{2}$ invariants, which provide more additional information of the topological superconductors than the Chern numbers provide. With the $\mathbf{Z}_{2}$ invariant, we define weak and strong topological superconductors in 2D systems. Moreover, we explain the causes of mismatch between the Chern numbers and the numbers of boundary states in topological superconductors, and claim that the robust Majorana zero modes are characterized by the $\mathbf{Z}_{2}$ invariant rather than the Chern numbers. We also extend the $\mathbf{Z}_{2}$ invariants to 3D non-time-reversal symmetry superconductor systems including gapful and gapless situations.
