标题： 从分数边界电荷到量子化霍尔电导 显示英文标题

标题： From fractional boundary charges to quantized Hall conductance

摘要： 我们研究在周期性调制的化学势存在下纳米线中出现的分数边界电荷（FBCs），并将它们与在垂直磁场存在的整数量子霍尔效应（QHE）区域二维电子气中出现的FBCs联系起来。 首先，我们表明在纳米线中，FBCs取分数值，并随着调制化学势的相位偏移线性变化。 这个线性斜率取由调制周期决定的量化值，并且仅取决于填充带的数量。 接下来，我们建立从一维系统到QHE设置的映射，在此我们再次关注FBCs的性质。 通过考虑类似于Laughlin构造的具有外部通量的圆柱拓扑结构，我们发现FBCs随通量变化的斜率是线性的，并且在任意无序存在的情况下也表现出普遍的量化值。 我们证明量化斜率导致了霍尔电导的量化。 重要的是，通过FBCs的方法适用于任意通量值和无序。 FBCs的斜率在清洁和无序的QHE系统中起着拓扑不变量的作用。 我们对FBCs的预测可以在整数QHE区域的纳米线和Corbino盘几何结构中进行实验验证。 显示英文摘要

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.