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arXiv 1501.03391cond-mat.mes-hallcond-mat.str-el
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泵浦电导、本征反常霍尔效应和拓扑不变量的统计

Pumping conductance, the intrinsic anomalous Hall effect, and statistics of topological invariants

Jan Dahlhaus, Roni Ilan, Daniel Freed, Michael Freedman, Joel E. Moore

摘要:

一个无序的二维陈氏绝缘体的泵浦电导的规模与增加的大小和固定的无序强度急剧高原过渡在普通和量子霍尔绝缘体之间的明确定义的能量。当无序强度随着系统尺寸的增加而缩小到零时,波动的陈数的“金属”状态可以扩展到整个能带。一个简单的论点导致一种加权均分的Chern数在一个有限的系统与周期性边界条件的迷你带:即使必须有很强的涨落之间的无序实现,在一个给定的能量的平均Chern数是由{ \it clean} Berry曲率分布预期从金属的固有反常霍尔效应公式。这种估计相比,使用最近开发的算子代数方法的数值结果,实际上占主导地位的平均陈数的变化是由内在的异常霍尔效应解释。数学附录提供了更精确的定义和陈数的完全分布模型。

英文摘要:

The pumping conductance of a disordered two-dimensional Chern insulator scales with increasing size and fixed disorder strength to sharp plateau transitions at well-defined energies between ordinary and quantum Hall insulators. When the disorder strength is scaled to zero as system size increases, the "metallic" regime of fluctuating Chern numbers can extend over the whole band. A simple argument leads to a sort of weighted equipartition of Chern number over minibands in a finite system with periodic boundary conditions: even though there must be strong fluctuations between disorder realizations, the mean Chern number at a given energy is determined by the {\it clean} Berry curvature distribution expected from the intrinsic anomalous Hall effect formula for metals. This estimate is compared to numerical results using recently developed operator algebra methods, and indeed the dominant variation of average Chern number is explained by the intrinsic anomalous Hall effect. A mathematical appendix provides more precise definitions and a model for the full distribution of Chern numbers.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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