Observing topological edge states in graphene using STM wavefront dislocations

We propose a way to systematically measure topological winding numbers in 2D materials with chiral symmetry. We consider the example of graphene with a vacancy, and we prove that it is topological according to the tenfold classification generalised to defects by Teo and Kane. As a result of bulk-edge correspondence, topological edge states appear in the spectrum (zero modes) and are localised around the vacancy. These edge states and their topological winding number are fully characterised by the readout of wavefront dislocations in STM data. Comparison with STM pictures of other (non topological) defects, e.g. adatoms, is discussed.