Transport properties of 2D graphene containing structural defects

We propose an extensive report on the simulation of electronic transport in 2D graphene in presence of structural defects. Amongst the large variety of such defects in sp$^2$ carbon-based materials, we focus on the Stone-Wales defect and on two divacancy-type reconstructed defects. First, based on ab initio calculations, a tight-binding model is derived to describe the electronic structure of these defects. Then, semiclassical transport properties including the elastic mean free paths, mobilities and conductivities are computed using an order-N real-space Kubo-Greenwood method. A plateau of minimum conductivity ($σ^{min}_{sc}= 4e^2/πh$) is progressively observed as the density of defects increases. This saturation of the decay of conductivity to $σ^{min}_{sc}$ is associated with defect-dependent resonant energies. Finally, localization phenomena are captured beyond the semiclassical regime. An Anderson transition is predicted with localization lengths of the order of tens of nanometers for defect densities around 1%.

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