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Lattices with a basis can host crystallographic defects which share the same topological charge (e.g.~the Burgers vector $vec b$ of a dislocation) but differ in their microscopic structure of the core. We demonstrate that in insulators with particle-hole symmetry and an odd number of orbitals per site, the microscopic details drastically affect the electronic structure: modifications can create or annihilate non-trivial 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.
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 anoma
The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather
We consider a 3-dimensional (3D) non-Hermitian exceptional line semimetal model and take open boundary conditions in x, y, and z directions separately. In each case, we calculate the parameter regions where the bulk-boundary correspondence is broken.
The chiral hinge modes are the key feature of a second order topological insulator in three dimensions. Here we propose a quadrupole index in combination of a slab Chern number in the bulk to characterize the flowing pattern of chiral hinge modes alo
Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline topological superconductors, we establish a bulk-boundary correspondenc