Ordinary lattice defects as probes of topology
In addition to topological lattice defects such as dislocations and disclinations, crystals are also accompanied by unavoidable ordinary defects, devoid of any non-trivial geometry or topology, among which vacancies, Schottky defects, substitutions, interstitials, and Frenkel pairs are the most common. In this work, we demonstrate that these ubiquitous ordinary lattice defects, although geometrically trivial, can nonetheless serve as universal probes of the non-trivial topology of electronic Bloch bands, and any change in the local topological environment in an otherwise normal insulator in terms of mid-gap bound states in their vicinity. We theoretically establish these generic findings by implementing a minimal model Hamiltonian describing time-reversal symmetry breaking topological and normal insulators on a square lattice, fostering such point defects. The defect-bound mid-gap modes are also shown to be robust against sufficiently weak random point-like charge impurities. Furthermore, we showcase experimental observation of such bound states by embedding ordinary crystal defects in two-dimensional acoustic Chern lattices, where precision-controlled hopping amplitudes are implemented via active meta-atoms and Green's-function-based spectroscopy is used to reconstruct spectra and eigenstates. Our combined theory-experiment study establishes ordinary lattice defects as probes of topology that should be germane in crystals of any symmetry and dimension, raising the possibility of arresting localized Majorana modes near such defects in the bulk of topological superconductors and to emulate ordinary-defect-engineered topological devices.