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

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.

10 pages, 12 figures

References in corpus (5)

• Quantum-limited shot noise in graphene
• Topological delocalization of two-dimensional massless Dirac fermions
• Effective contact model for transport through weakly-doped graphene
• Transport through normal metal - graphene contacts
• Chalker-Coddington model described by an S-matrix with odd dimensions

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• Majorana quasiparticles of inhomogeneous Rashba chain
• Fate of topological states and mobility edges in one-dimensional slowly varying incommensurate potentials
• Local density of states in disordered graphene
• Light-modulated Josephson effect in Kekulé patterned graphene
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch
• Unitarization of Pseudo-Unitary Quantum Circuits in the S-matrix Framework
• Tunable Topological Phases in Quantum Kirigamis