Delocalization of 2D Dirac Fermions: The Role of a Broken Supersymmetry

The mechanism of delocalization of two-dimensional Dirac fermions with random mass is investigated, using a superfield representation. Although localization effects are very strong, one fermion component can delocalize due to the spontaneous breaking of a special supersymmetry of the model. The delocalized fermion has a nonsingular density of states and is described by a diffusion propagator. Supersymmetry is restored if the mean of the random mass is sufficiently large. This is accompanied by a critical boson component.