Bulk-defect correspondence in particle-hole symmetric insulators and semimetals

The presence of topological zero modes in dislocations is usually thought to be independent of local details and determined by topological invariants. We demonstrate that in insulators with particle-hole symmetry and an odd number of orbitals per site, changes in the microscopic details of the dislocation core can affect the electronic structure drastically without changing the topological charge of the defect (the Burgers vector), creating or annihilating nontrivial bound states with an associated fractional charge. We show that this observation is related to the behavior of end modes of a dimerized chain and discuss how the end or defect states are predicted from topological invariants in these more complicated cases. Furthermore, using explicit examples on the honeycomb lattice, we explain how bound states in vacancies, dislocations, and disclinations are related to each other and to edge modes and how similar features arise in nodal semimetals such as graphene.