Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model

TL;DR

This paper develops a numerical method using the Chalker-Coddington network model to calculate the conductance of graphene sheets, effectively handling intervalley scattering and disorder effects without requiring smooth potentials.

Contribution

It introduces a novel application of the network model to solve scattering problems in graphene, bypassing computationally expensive regions and avoiding intervalley scattering.

Findings

Network model accurately computes conductance in graphene.

Conductance increases with disorder, consistent with prior research.

Method avoids the need for smooth potentials unlike tight-binding models.

Abstract

The Chalker-Coddington network model (introduced originally as a model for percolation in the quantum Hall effect) is known to map onto the two-dimensional Dirac equation. Here we show how the network model can be used to solve a scattering problem in a weakly doped graphene sheet connected to heavily doped electron reservoirs. We develop a numerical procedure to calculate the scattering matrix with the aide of the network model. For numerical purposes, the advantage of the network model over the honeycomb lattice is that it eliminates intervalley scattering from the outset. We avoid the need to include the heavily doped regions in the network model (which would be computationally expensive), by means of an analytical relation between the transfer matrix through the weakly doped region and the scattering matrix between the electron reservoirs. We test the network algorithm by calculating the conductance of an electrostatically defined quantum point contact and comparing with the tight-binding model of graphene. We further calculate the conductance of a graphene sheet in the presence of disorder in the regime where intervalley scattering is suppressed. We find an increase in conductance that is consistent with previous studies. Unlike the tight-binding model, the network model does not require smooth potentials in order to avoid intervalley scattering.