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arXiv 1602.05039cond-mat.mes-hall
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高能电子在量子霍尔边缘态弛豫的统计理论

Statistical theory of relaxation of high energy electrons in quantum Hall edge states

Anders Mathias Lunde, Simon E. Nigg

摘要:

我们从理论上研究了整数量子霍尔体系中两个自旋极化方向相反的非平衡边缘态电子之间的能量交换。隧道耦合到边缘态之一的量子点以高能量局部注入电子。因此,在费米能级以上的高能量处产生能量分布中的窄峰。第二下游量子点执行电子分布函数的能量分辨测量。通过改变两个点之间的距离,我们能够跟踪边缘状态之间的能量交换和弛豫的每一步-甚至在某些条件下进行分析。在沿着边缘不存在平移不变性的情况下,例如由于无序的存在,能量可以通过非动量守恒的两粒子碰撞来交换。对于弱破缺的平移不变性,我们证明了弛豫是由耦合的Fokker-Planck方程描述。从这些我们发现,注入电子的弛豫可以理解为一个广义的漂移扩散过程中的能量空间,我们确定的漂移速度和动力学扩散参数统计。最后,我们提供了一个物理上有吸引力的图片在个人的边缘状态加热作为结果的注入电子的弛豫。

英文摘要:

We investigate theoretically the energy exchange between electrons of two co-propagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states - even analytically under certain conditions. In the absence of translational invariance along the edge, e.g. due to the presence of disorder, energy can be exchanged by non-momentum conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift-velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge state heating as a result of the relaxation of the injected electrons.

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