  The response of glasses to mechanical loading often leads to the formation of
inhomogeneous flow patterns that strongly affect materials properties. Among
them, shear bands are ubiquitous in a wide variety of materials, ranging from
soft matter systems to metallic alloys. Shear banding is associated with strain
localization, i.e. the deformation of the sheared glassy solid is localized in
space in form of band-like structures. These structures are often precursors to
catastrophic failure, implying that a proper understanding of the underlying
mechanisms could lead to the design of smarter materials. However, despite its
importance in material science, the microscopic origin of shear banding in
glassy materials is only poorly understood. Here, the formation of shear
banding in glassy systems is revealed by non-equilibrium molecular dynamics
simulations (NEMD) of a binary Lennard-Jones mixture, subject to a constant
strain rate. In its glass state, this system exhibits for all considered strain
rates the formation of a percolating cluster of mobile regions at a critical
strain. We show that this percolation transition belongs to the universality
class of directed percolation. Only at low shear rates, where the steady-state
stress is close to the yielding threshold, the percolating cluster evolves into
a transient (but long-lived) shear band with a diffusive growth of its width.
