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arXiv 1606.09436cond-mat.mes-hall
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存在局域缺陷时的弹道量子输运理论

Theory of ballistic quantum transport in presence of localized defects

K. Kolasiński, A. Mreńca-Kolasińska, B. Szafran

摘要:

我们提出了一种有效的数值方法来处理跨设备的弹道量子输运,该输运由指定为具有局部潜在缺陷的系统的紧束缚(TB)汉密尔顿描述。该方法是基于波函数匹配方法,Lippmann-Schwinger方程(LEQ)和散射矩阵形式主义。我们表明,格林函数的矩阵元素的数量进行评估的未扰动系统,可以从根本上减少投影的时间逆散射波函数从根本上提高了速度,降低了内存消耗的计算。我们的方法可以应用于任意几何形状的量子器件和任何数量的自由度或引线连接。我们提供了一对夫妇的理论可能的应用,包括电流平衡在石墨烯的pn结和扫描门显微镜映射的电子轨迹在磁聚焦实验的石墨烯带的例子。此外,我们提供了一个简单的玩具的例子,电子输运通过一维线添加现场扰动,并获得一个简单的公式,电导表明,格林函数的设备可以从电导与杂质强度特性。

英文摘要:

We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function matching approach, Lippmann-Schwinger equation (LEQ) and the scattering matrix formalism. We show that the number of matrix elements of the Green's function to be evaluated for the unperturbed system can be essentially reduced by projection of the time reversed scattering wave functions on LEQ which radically improves the speed and lowers the memory consumption of the calculations. Our approach can be applied to quantum devices of an arbitrary geometry and any number of degrees of freedom or leads attached. We provide a couple of examples of possible applications of the theory, including current equilibration at the p-n junction in graphene and scanning gate microscopy mapping of electron trajectories in the magnetic focusing experiment on a graphene ribbon. Additionally, we provide a simple toy example of electron transport through 1D wire with added onsite perturbation and obtain a simple formula for conductance showing that Green's function of the device can be obtained from the conductance versus impurity strength characteristics.

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