Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

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 rst 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 rst-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.

The provided repository contains all code and data to reproduce the numerical results of this study.