Scaling near random criticality in two-dimensional Dirac fermions

TL;DR

This paper investigates the scaling behavior of two-dimensional Dirac fermions with randomness, revealing a critical line with diverging localization length at zero energy, and introduces fractional dimensionality in localization properties.

Contribution

It demonstrates the existence of a random critical line in 2D Dirac fermions and explores its scaling properties, including fractional dimensionality effects.

Findings

Localization length diverges at zero energy for the RH model

Generalized Ohm's law observed in fractional dimensions

All states are localized except at zero energy in the models

Abstract

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.