  The microscopic mechanism by which amorphous solids yield plastically under
an externally applied stress or deformation has remained elusive in spite of
enormous research activity in recent years. Most approaches have attempted to
identify atomic-scale structural "defects" or spatio-temporal correlations in
the undeformed glass that may trigger plastic instability. In contrast, here we
show that the topological defects which are responsible for the plastic
instability can be identified, not in the static structure of the glass, but
rather in the nonaffine displacement field under deformation. These
dislocation-like topological defects (DTDs) can be quantitatively characterized
in terms of Burgers circuits (and the resulting Burgers vectors) which are
constructed on the microscopic nonaffine displacement field. We demonstrate
that (i) DTDs are the manifestation of incompatibility of deformation in
glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the
resulting average Burgers vector displays peaks in correspondence of major
plastic events, including a spectacular non-local peak at the yielding
transition, which results from self-organization into shear bands due to the
attractive interaction between anti-parallel DTDs; (iii) application of
Schmid's law to the DTDs leads to prediction of shear bands at 45 degrees for
uniaxial deformations, as widely observed in experiments and simulations.
