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arXiv 1302.6178cond-mat.mes-hall
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沿边界的磁输运:从相干电子聚焦到边缘沟道输运

Magnetotransport along a boundary: From coherent electron focusing to edge channel transport

Thomas Stegmann, Dietrich E. Wolf, Axel Lorke

摘要:

我们从理论上研究了如何电子,相干注入在一个点上的边界上的二维电子系统,由一个垂直磁场$B$聚焦到另一个点上的边界。利用非平衡格林函数方法,计算了广义四点霍尔电阻$R_{xy}$随B的变化。在弱场中,$R_{xy}$显示出实验中观察到的特征等距峰,并通过沿边界的经典回旋运动来解释。在强磁场中,$R_{xy}$显示出反映量子霍尔效应的单一扩展平台。在中间场,我们发现叠加在低霍尔平台的异常振荡,这既不是周期性的1/B(量子霍尔效应),也不是在$B$(经典回旋运动)。这种振荡可以用占用的边缘信道之间的干扰来解释,这会导致$R_{xy}$中的跳动。在两个被占用的边缘通道的情况下,这些拍频构成了封闭在边缘通道内的磁通量与通量量子之间的新的可伸缩性。引入退相干和部分镜面边界表明,这种新的效果是相当强大的。

英文摘要:

We study theoretically how electrons, coherently injected at one point on the boundary of a two-dimensional electron system, are focused by a perpendicular magnetic field $B$ onto another point on the boundary. Using the non-equilibrium Green's function approach, we calculate the generalized 4-point Hall resistance $R_{xy}$ as a function of B. In weak fields, $R_{xy}$ shows the characteristic equidistant peaks observed in the experiment and explained by classical cyclotron motion along the boundary. In strong fields, $R_{xy}$ shows a single extended plateau reflecting the quantum Hall effect. In intermediate fields, we find superimposed upon the lower Hall plateaus anomalous oscillations, which are neither periodic in 1/B (quantum Hall effect) nor in $B$ (classical cyclotron motion). The oscillations are explained by the interference between the occupied edge channels, which causes beatings in $R_{xy}$. In the case of two occupied edge channels, these beatings constitute a new commensurability between the magnetic flux enclosed within the edge channels and the flux quantum. Introducing decoherence and a partially specular boundary shows that this new effect is quite robust.

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