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

TL;DR

This paper explores how lattice defects called disclinations in rotation-symmetric topological insulators and superconductors host anomalous states, linking bulk topology to defect-bound states through a comprehensive classification.

Contribution

It introduces a framework connecting disclination states to bulk topological phases across all symmetry classes in 2D and 3D, extending the understanding of topological defect-bound states.

Findings

Disclination states include Majorana zero-modes and helical states.

The classification covers all Cartan symmetry classes in 2D and 3D.

The bulk-boundary-disclination correspondence is clarified and extended.

Abstract

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.