论文标题
$ pt $ - invariant拓扑和二阶节点半按半学的边界关键性
Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
论文作者
论文摘要
对于常规的拓扑阶段，无边界模式由散装拓扑不变式确定。基于开发一种解决高阶边界模式的分析方法，我们提出了$ pt $ invariant $ 2 $ D拓扑绝缘子和$ 3 $ D的拓扑半学，超出了这个散装式的信件框架。随着散装不变的拓扑不变，其一阶边界经历了用二阶边界零模型分开不同相的过渡。对于$ 2 $ d的拓扑绝缘子，螺旋边缘模式出现在两个二阶拓扑绝缘体阶段的过渡点，分别具有对角线和偏角零角。因此，对于$ 3 $ d的拓扑半学，关键性对应于狄拉克半学相的表面螺旋式弧形。有趣的是，我们发现$ 3 $ d的系统通常属于新型的二阶节结线半学相，具有张开的表面，但一对对角线或外铰链铰链Fermi Arcs。
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 $2$D topological insulators and $3$D topological semimetals that go beyond this bulk-boundary correspondence framework. With unchanged bulk topological invariant, their first-order boundaries undergo transitions separating different phases with second-order-boundary zero-modes. For the $2$D 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 $3$D topological semimetal, the criticality corresponds to surface helical Fermi arcs of a Dirac semimetal phase. Interestingly, we find that the $3$D 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.
