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.
We study transport properties of a Chalker-Coddington type model in the plane which presents asymptotically pure anti-clockwise rotation on the left and clockwise rotation on the right. We prove delocalisation in the sense that the absolutely continuous spectrum covers the whole unit circle. The result is of topological nature and independent of the details of the model.
Finite Size Scaling of the Chalker-Coddington Model
在参考文献1（物理评论B 80，041304（R）（2009））中，我们报告了量子霍尔跃迁处局域化长度发散的临界指数的估计值，该估计值明显大于其他作者先前发表的工作中报告的值。在本文中，我们更新了我们的有限尺寸标度的Chalker-Coddington模型的分析，并提出了以前的低估其他作者的起源。我们还将我们的结果与Lütken和Ross的预测（Physics Letters B 653，363（2007））进行了比较。
Recent high-precision results for the critical exponent of the localization length at the integer quantum Hall (IQH) transition differ considerably between experimental ($ν_\text{exp} \approx 2.38$) and numerical ($ν_\text{CC} \approx 2.6$) values obtained in simulations of the Chalker-Coddington (CC) network model. We revisit the arguments leading to the CC model and consider a more general network with geometric (structural) disorder. Numerical simulations of this new model lead to the value $ν\approx 2.37$ in very close agreement with experiments. We argue that in a continuum limit the geom…
