Scaling near random criticality in two-dimensional Dirac fermions

Details Scaling near random criticality in two-dimensional Dirac fermions Scaling near random criticality in two-dimensional Dirac fermions

1998-07-02

arxiv.org/abs/cond-mat/9807029v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

RevTeX with 4 postscript figures, To appear in Physical Review B

Scientific paper

10.1103/PhysRevB.58.6680

Recently the existence of a random critical line in two dimensional Dirac fermions is confirmed. In this paper, we focus on its scaling properties, especially in the critical region. We treat Dirac fermions in two dimensions with two types of randomness, a random site (RS) model and a random hopping (RH) model. The RS model belongs to the usual orthogonal class and all states are localized. For the RH model, there is an additional symmetry expressed by ${\{}{\cal H},{\gamma}{\}}=0$. Therefore, although all non-zero energy states localize, the localization length diverges at the zero energy. In the weak localization region, the generalized Ohm's law in fractional dimensions, $d^{*}(<2)$, has been observed for the RH model.

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