Random resistor network model of minimal conductivity in graphene

TL;DR

This paper introduces a random resistor network model to analyze how doping, disorder, and magnetic effects influence the minimal conductivity in undoped graphene, emphasizing the role of charge fluctuations and P-N junctions.

Contribution

It presents a novel resistor network model that captures the scaling behavior of conductivity and magnetoresistance in graphene with charge density fluctuations.

Findings

Conductance scales with doping and disorder levels.

P-N junction transmissions are crucial for macroscopic conductivity.

Model explains quantum magnetoresistance and dephasing in graphene.

Abstract

Transport in undoped graphene is related to percolating current patterns in the networks of {\em N-} and {\em P}-type regions reflecting the strong bipolar charge density fluctuations. Transmissions of the {\em P-N} junctions, though small, are vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.