Wang Kai, Dai Jia-Xiao, Shao L B, Yang Shengyuan A, Zhao Y X
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.
Phys Rev Lett. 2020 Sep 18;125(12):126403. doi: 10.1103/PhysRevLett.125.126403.
For conventional topological phases, the boundary gapless modes are determined by bulk topological invariants. Based on developing an analytic method to solve higher-order boundary modes, we present PT-invariant 2D topological insulators and 3D topological semimetals that go beyond this bulk-boundary correspondence framework. With unchanged bulk topological invariants, their first-order boundaries undergo transitions separating different phases with second-order boundary zero modes. For the 2D topological insulator, the helical edge modes appear at the transition point for two second-order topological insulator phases with diagonal and off-diagonal corner zero modes, respectively. Accordingly, for the 3D topological semimetal, the criticality corresponds to surface helical Fermi arcs of a Dirac semimetal phase. Interestingly, we find that the 3D system generically belongs to a novel second-order nodal-line semimetal phase, possessing gapped surfaces but a pair of diagonal or off-diagonal hinge Fermi arcs.
对于传统拓扑相，边界无隙模式由体拓扑不变量决定。基于开发一种解析方法来求解高阶边界模式，我们提出了超越这种体-边界对应框架的PT不变二维拓扑绝缘体和三维拓扑半金属。在体拓扑不变量不变的情况下，它们的一阶边界经历转变，分离出具有二阶边界零模式的不同相。对于二维拓扑绝缘体，螺旋边缘模式出现在分别具有对角和非对角角零模式的两个二阶拓扑绝缘体相的转变点处。相应地，对于三维拓扑半金属，临界性对应于狄拉克半金属相的表面螺旋费米弧。有趣的是，我们发现三维系统一般属于一种新型的二阶节线半金属相，具有带隙表面但有一对对角或非对角铰链费米弧。
