## Abstract

Using an exact mapping to disordered Coulomb gases, we introduce a method to study two-dimensional Dirac fermions with quenched disorder in two dimensions that allows us to treat nonperturbative freezing phenomena: For purely random gauge disorder it is known that the exact zero-energy eigenstate exhibits a freezinglike transition at a threshold value of disorder σ = σ_{th} = 2. Here we compute the dynamical exponent z that characterizes the critical behavior of the density of states around zero energy, and find that it also exhibits a phase transition. Specifically, we find that ρ(E=O+iε)∼ε^{2/z-1} [and ρ(E)∼E^{2/z-1}] with z=1 + σ for σ <2 and z= √8σ-1 for σ > 2. For a finite system size L < ε^{-1/z} we find large sample to sample fluctuations with a typical ρε(O)∼L^{z-2}. Adding a scalar random potential of small variance δ, as in the corresponding quantum Hall system, yields a finite noncritical ρ(O) ∼ δ^{a} whose scaling exponent a exhibits two transitions, one at σ_{th}/4 and the other at σ_{th}. These transitions are shown to be related to the one of a directed polymer on a Cayley tree with random signs (or complex) Boltzmann weights. Some observations are made for the strong disorder regime relevant to describe transport in the quantum Hall system.

Original language | English |
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Article number | 125323 |

Pages (from-to) | 1253231-12532310 |

Number of pages | 11279080 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 65 |

Issue number | 12 |

DOIs | |

State | Published - 15 Mar 2002 |

## ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics