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Journal of Statistical Physics

, Volume 171, Issue 4, pp 696–726 | Cite as

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

  • Luigi Barletti
  • Claudia Negulescu
Article
  • 55 Downloads

Abstract

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 is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

Keywords

Transmission conditions Graphene Diffusion limit Boundary layer Milne problem 

Notes

Acknowledgements

Support is acknowledged from the Italian-French project Projet International de Coopration Scientifique (PICS) “MANUS—Modelling and Numerics for Spintronics and Graphene” (Ref. PICS07373).

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Authors and Affiliations

  1. 1.Dipartimento di Matematica e Informatica “U. Dini”FlorenceItalia
  2. 2.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouseFrance

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