论文标题
石墨烯中扩散传输的量子传输条件，具有陡峭的电势
Quantum transmission conditions for diffusive transport in graphene with steep potentials
论文作者
论文摘要
我们提出了在石墨烯中用于固定电子传输的漂移扩散模型的形式推导，在存在较高的电势轮廓（例如障碍物和步骤）的情况下。假设电势可以在宏观尺度上具有陡峭宽度的宽度变化，则将这种条形视为量子界面，将经典区域沿其左侧和右侧耦合。在假定电势平滑的两个经典区域中，用半经典动力学方程描述了电子和孔传输。动力学模型的扩散极限是通过希尔伯特膨胀和边界层分析得出的，由经典区域中的漂移扩散方程组成，并由量子扩散的传输条件通过界面。边界层分析导致讨论一个四倍的米尔恩（半空间，半程）传输问题。
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.
