arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1809.00538cond-mat.mes-hallcond-mat.str-el
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从分数边界电荷到量子化霍尔电导

From fractional boundary charges to quantized Hall conductance

Manisha Thakurathi, Jelena Klinovaja, Daniel Loss

摘要:

我们研究了周期性调制化学势存在下纳米线中的分数边界电荷(FBCs),并将其与整数量子霍尔效应(QHE)机制中垂直磁场存在下二维电子气中的分数边界电荷联系起来.首先,我们表明,在纳米线的FBCs采取分数值和线性变化的调制化学势的相位偏移的函数。该线性斜率采用由调制周期确定的量化值,并且仅取决于填充带的数量。接下来,我们建立了从一维系统到QHE设置的映射,在那里我们再次关注FBCs的属性。通过考虑一个类似于Laughlin结构的外部通量的圆柱拓扑,我们发现FBCs作为通量的函数的斜率是线性的,并且假设了普遍的量子化值,也存在任意的无序。我们建立了量子化的斜率引起的霍尔电导的量子化。重要的是,通过FBCs的方法是有效的任意通量值和无序。FBCs的斜率对于清洁和无序QHE系统起着拓扑不变量的作用。我们的预测FBCs可以在纳米线和Corbino磁盘几何形状的整数QHE制度的实验测试。

英文摘要:

We study the fractional boundary charges (FBCs) occurring in nanowires in the presence of periodically modulated chemical potentials and connect them to the FBCs occurring in a two-dimensional electron gas in the presence of a perpendicular magnetic field in the integer quantum Hall effect (QHE) regime. First, we show that in nanowires the FBCs take fractional values and change linearly as a function of phase offset of the modulated chemical potential. This linear slope takes quantized values determined by the period of the modulation and depends only on the number of the filled bands. Next, we establish a mapping from the one-dimensional system to the QHE setup, where we again focus on the properties of the FBCs. By considering a cylinder topology with an external flux similar to the Laughlin construction, we find that the slope of the FBCs as function of flux is linear and assumes universal quantized values, also in the presence of arbitrary disorder. We establish that the quantized slopes give rise to the quantization of the Hall conductance. Importantly, the approach via FBCs is valid for arbitrary flux values and disorder. The slope of the FBCs plays the role of a topological invariant for clean and disordered QHE systems. Our predictions for the FBCs can be tested experimentally in nanowires and in Corbino disk geometries in the integer QHE regime.

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