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首页> 外文期刊>Journal of Computational Physics >Monte Carle simulation of quantum transport through nanostructures
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Monte Carle simulation of quantum transport through nanostructures

机译：通过纳米结构进行量子传输的蒙特卡洛模拟

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摘要

We describe a numerical scheme of combining Monte Carlo procedure and quantum scattering theory to simulate electron transport processes through nanostructures. The transport of electrons through a nanostructure is a highly nontrivial nonequilibrium process in which we should consider the interplay of (i) complicated many-body quantum states in nanostructure, (ii) thermal relaxation processes keeping the leads (electron reservoirs) in local equilibrium, (iii) the coupling between the leads and the nanostructure, and (iv) the bias causing nonequilibrium, current, and evolution of quantum states in the nanostructure. Considering the quantum coherence within the nanostructure, we include the degrees of freedom of the nanostructure and a single tunneling electron and solve the Schr?dinger equation for the many-body states to obtain the scattering matrix in the Fock space from which both the transmission of the electron and the variation of the states in nanostructure can be full quantum-mechanically calculated. The transport is investigated by the Monte Carlo simulation of successive scattering events of single electrons which are sampled with the Metropolis scheme governed by the scattering probabilities, the thermal statistics in the leads, and the applied bias. By this way from a given initial nanostructure state we can calculate the time evolutions of the current and the internal state. As examples we investigate the transmission of electrons through a two-level system. It is shown that the proposed method can properly deal with the inelastic effects in transport processes.
机译：我们描述了一种结合了蒙特卡罗过程和量子散射理论的数值方案，以模拟通过纳米结构的电子传输过程。电子通过纳米结构的传输是一个非常重要的非平衡过程，在该过程中，我们应考虑（i）纳米结构中复杂的多体量子态的相互作用，（ii）使引线（电子储库）保持局部平衡的热弛豫过程， （iii）引线与纳米结构之间的耦合，以及（iv）导致纳米结构中的不平衡，电流和量子态演化的偏压。考虑到纳米结构内的量子相干性，我们包括了纳米结构和单个隧穿电子的自由度，并求解了多体态的薛定er方程，从而获得了Fock空间中的散射矩阵，从该矩阵可知电子和纳米结构中状态的变化可以通过量子力学完全计算出来。通过蒙特卡洛模拟法对单个电子的连续散射事件进行了研究，这些散射事件是通过Metropolis方案采样的，该方案受散射概率，导线中的热统计和所施加的偏压控制。通过给定的初始纳米结构状态，我们可以计算电流和内部状态的时间演化。作为示例，我们研究了电子通过两能级系统的传输。结果表明，所提出的方法可以正确处理运输过程中的非弹性效应。

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