Tiwari Apoorv, Li Ming-Hao, Bernevig B A, Neupert Titus, Parameswaran S A
Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.
Condensed Matter Theory Group, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland.
Phys Rev Lett. 2020 Jan 31;124(4):046801. doi: 10.1103/PhysRevLett.124.046801.
We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting C_{2n}T symmetry upon the introduction of non-Abelian surface topological order. In both cases, the topological order on a single side surface breaks time-reversal symmetry, but appears with its time-reversal conjugate on alternating sides in a C_{2n}T preserving pattern. In the absence of the HOTI/HOTSC bulk, such a pattern necessarily involves gapless chiral modes on hinges between C_{2n}T-conjugate domains. However, using a combination of K-matrix and anyon condensation arguments, we show that on the boundary of a 3D HOTI/HOTSC these topological orders are fully gapped and hence "anomalous." Our results suggest that new patterns of surface and hinge states can be engineered by selectively introducing topological order only on specific surfaces.
我们表明，在三维高阶拓扑绝缘体（HOTIs）和超导体（HOTSCs）中，手性狄拉克和马约拉纳棱模可以被能隙化，同时在引入非阿贝尔表面拓扑序时保持保护的(C_{2n}T)对称性。在这两种情况下，单侧表面上的拓扑序打破了时间反演对称性，但以其时间反演共轭形式出现在交替的面上，形成一种保持(C_{2n}T)的模式。在没有HOTI/HOTSC体的情况下，这种模式必然涉及(C_{2n}T)共轭域之间棱上的无隙手性模。然而，通过结合K矩阵和任意子凝聚论证，我们表明在三维HOTI/HOTSC的边界上，这些拓扑序是完全能隙化的，因此是“反常的”。我们的结果表明，可以通过仅在特定表面上选择性地引入拓扑序来设计新的表面和棱态模式。
