Spotting structural defects in crystals from topology of vibrational modes

Because of the inevitably disordered background, structural defects are not well-defined concepts in amorphous solids. In order to overcome this difficulty, it has been recently proposed
that topological defects can be still identified in the pattern of vibrational modes, by looking at the corresponding eigenvector field at low frequency. Moreover, it has been verified that
these defects strongly correlate with the location of soft spots in glasses, that are the regions more prone to plastic rearrangements. Here, we show that the topology of vibrational modes
predicts the location of structural defects in crystals as well, including the cases of dislocations, disclinations and Eshelby inclusions. Our results suggest that in crystalline solids topological
defects in the vibrational modes are directly connected to the well-established structural defects governing plastic deformations and present characteristics very similar to those observed in
amorphous solids.