  Oppositely driven binary particles with repulsive interactions on the square
lattice are investigated at the zero-temperature limit. Two classes of steady
states related to stuck configurations and lane formations have been
constructed in systematic ways under certain conditions. A mean-field type
analysis carried out using a percolation problem based on the constructed
steady states provides an estimation of the phase diagram, which is
qualitatively consistent with numerical simulations. Further, finite size
effects in terms of lane formations are discussed.
