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Phys Rev Lett. 2017 Dec 15;119(24):246401. doi: 10.1103/PhysRevLett.119.246401. Epub 2017 Dec 11.

Reflection-Symmetric Second-Order Topological Insulators and Superconductors.

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Dahlem Center for Complex Quantum Systems and Physics Department, Freie Universit├Ąt Berlin, Arnimallee 14, 14195 Berlin, Germany.


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.

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