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  • Title: Boundary Criticality of PT-Invariant Topology and Second-Order Nodal-Line Semimetals.
    Author: Wang K, Dai JX, Shao LB, Yang SA, Zhao YX.
    Journal: Phys Rev Lett; 2020 Sep 18; 125(12):126403. PubMed ID: 33016751.
    Abstract:
    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.
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