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The response of glasses to mechanical loading often leads to the formation ofinhomogeneous flow patterns that strongly affect materials properties. Amongthem, shear bands are ubiquitous in a wide variety of materials, ranging fromsoft matter systems to metallic alloys. Shear banding is associated with strainlocalization, i.e. the deformation of the sheared glassy solid is localized inspace in form of band-like structures. These structures are often precursors tocatastrophic failure, implying that a proper understanding of the underlyingmechanisms could lead to the design of smarter materials. However, despite itsimportance in material science, the microscopic origin of shear banding inglassy materials is only poorly understood. Here, the formation of shearbanding in glassy systems is revealed by non-equilibrium molecular dynamicssimulations (NEMD) of a binary Lennard-Jones mixture, subject to a constantstrain rate. In its glass state, this system exhibits for all considered strainrates the formation of a percolating cluster of mobile regions at a criticalstrain. We show that this percolation transition belongs to the universalityclass of directed percolation. Only at low shear rates, where the steady-statestress is close to the yielding threshold, the percolating cluster evolves intoa transient (but long-lived) shear band with a diffusive growth of its width.

Formation and growth of shear bands in glasses: existence of an underlying directed percolation transition