We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct $d$-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to $(d-2)$-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.
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- 1 Freie Universität Berlin / Freie Universität Berlin [FU Berlin]
- 2 Niels Bohr Institute [NBI]
- 3 Leibniz-Institut für Festkörper- und Werkstoffforschung Dresden / Leibniz Institute for Solid State and Materials Research [IFW]
- 4 Technische Universiteit Delft / Delft University of Technology [TU Delft]
- 5 Polska Akademia Nauk / Polish Academy of Sciences [PAN]