Exact Solutions Describing Collapse of Landau Levels in Graphene

The eigenequation for single-layer graphene in transverse electric and perpendicular magnetic fields is investigated at a critical value |E| = υ _F B. The critical solutions are not bound states and contain two unknown constants. Different from the case of the “classical” Hall effect, the electric current in the direction perpendicular to the electric and magnetic fields could be positive or negative depending on the values of the unknown constants.