无序Dirac固体电子流中随机分支的出现及其动力学性质
Emergence and dynamical properties of stochastic branching in the electronic flows of disordered Dirac solids
摘要：
石墨烯以及更一般的狄拉克固体构成了电子流是超相对论的二维材料。当狄拉克固体沉积在不同的衬底表面粗糙度，局部随机电位的发展，通过不均匀的电荷杂质分布。这种外部电势深刻地影响了电荷流动，并诱导了电流分支的混乱模式，该模式通过由表面的随机性产生的聚焦和散焦效应而发展。可以使用附加偏置电压来调谐载流子电流的分支模式。我们采用分析和数值计算的方法来研究狄拉克固体中载流子分支的发生和统计特性。我们发现一个特定的缩放类型的关系，连接的物理规模的分支的发生与特征介质属性，如无序和偏置场。我们使用数值来测试和验证的理论预测，以及微扰的方法，给出了一个明确的指示制度的有效性的方法。这项工作是相关的设备应用程序，并可以进行实验测试。
英文摘要：
Graphene as well as more generally Dirac solids constitute two dimensional materials where the electronic flow is ultra relativistic. When a Dirac solid is deposited on a different substrate surface with roughness, a local random potential develops through an inhomogeneous charge impurity distribution. This external potential affects profoundly the charge flow and induces a chaotic pattern of current branches that develops through focusing and defocusing effects produced by the randomness of the surface. An additional bias voltage may be used to tune the branching pattern of the charge carrier currents. We employ analytical and numerical techniques in order to investigate the onset and the statistical properties of carrier branches in Dirac solids. We find a specific scaling-type relationship that connects the physical scale for the occurrence of branches with the characteristic medium properties, such as disorder and bias field. We use numerics to test and verify the theoretical prediction as well as a perturbative approach that gives a clear indication of the regime of validity of the approach. This work is relevant to device applications and may be tested experimentally.
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