Langbehn Josias, Peng Yang, Trifunovic Luka, von Oppen Felix, Brouwer Piet W
Dahlem Center for Complex Quantum Systems and Physics Department, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
Phys Rev Lett. 2017 Dec 15;119(24):246401. doi: 10.1103/PhysRevLett.119.246401. Epub 2017 Dec 11.
Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but with topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the existence of such second-order topological insulators in two and three dimensions. We show that reflection symmetry can be employed to systematically generate examples of second-order topological insulators and superconductors, although the topologically protected states at corners (in two dimensions) or at crystal edges (in three dimensions) continue to exist if reflection symmetry is broken. A three-dimensional second-order topological insulator with broken time-reversal symmetry shows a Hall conductance quantized in units of e^{2}/h.
二阶拓扑绝缘体是一种晶体绝缘体，其体态有能隙，晶界也有能隙，但在两条边界的交点处存在拓扑保护的无能隙态。在没有进一步空间对称性的情况下，十个阿尔特兰 - 齐恩鲍尔对称类中的五个允许在二维和三维中存在此类二阶拓扑绝缘体。我们表明，反射对称性可用于系统地生成二阶拓扑绝缘体和超导体的示例，不过，如果反射对称性被破坏，角点（二维中）或晶体边缘（三维中）的拓扑保护态仍然存在。一个具有破缺时间反演对称性的三维二阶拓扑绝缘体表现出以(e^{2}/h)为单位的量子化霍尔电导。
