Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

@article{Barletti2018QuantumTC,
  title={Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials},
  author={Luigi Barletti and Claudia Negulescu},
  journal={Journal of Statistical Physics},
  year={2018},
  volume={171},
  pages={696-726}
}
We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport… 
Mathematical modelling of charge transport in graphene heterojunctions
A typical graphene heterojunction device can be divided into two classical zones, where the transport is basically diffusive, separated by a "quantum active region" (e.g., a locally gated region),

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