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 -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.
- Received 12 May 2020
- Accepted 6 August 2020
DOI:https://doi.org/10.1103/PhysRevLett.125.126403
© 2020 American Physical Society
Physics Subject Headings (PhySH)
synopsis
A Twist in Topological Wisdom
Published 16 September 2020
New theoretical predictions overthrow the assumption that a material’s bulk topological properties are linked to the same properties at its surface.
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