Anderson localization for two-dimensional random hopping model with SU(2) symmetry Original Research Article

A two-dimensional random hopping model with SU(2) symmetry is studied. A pure model is assumed to have nodes in the dispersion relation, which leads in the continuum limit to the Dirac fermion with random potentials. The field theory at the band center is shown to be in the universality class of U(2n)/O(2n) and U(2n) nonlinear sigma model for the system with broken and unbroken time-reversal symmetry, respectively. Vanishing of the beta function implies extended states at the band center. Density of state is expected to be diverge for infinite systems, whereas for finite systems it should vanish as a cubic function of the energy at the band center for the former case, while linear for the latter.