Quantum Hall effect with realistic boundary conditions.
Quantum Hall effect with realistic boundary conditions.
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具有真实边界条件的量子霍尔效应。
DOI：
10.1103/physrevb.35.2188
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
M. Thouless
中科院分区：
文献类型：
--
作者：
Niu;M. Thouless
量子霍尔效应的早期理论依赖于边界条件（圆柱形，环形等）。其与实验装置的非常不同（基本上是条状的）。为了消除这种差异，我们表明，霍尔电导率具有指数局域性的费米能量位于体扩展状态的水平之间时，这是真实的，尽管在费米能量的边缘状态。我们详细描述了如何这种局部属性可以用来适应规范对称性参数的劳克林和拓扑不变的方法牛，无，吴的条件下，更接近真实的实验。由此得出的结论是，当系统尺寸与微观长度（通常是磁长度）相比较大时，对霍尔电导的量化的边界校正是指数小的。
Earlier theories of the quantum Hall effect depend on boundary conditions (cylindrical, toroidal, etc.) which are very different from that of the experimental devices (essentially striplike). To remove this discrepancy, we show that the Hall conductivity has an exponential locality property whenever the Fermi energy lies between the levels of the bulk extended states, and that this is true in spite of the edge states at the Fermi energy. We describe in detail how this locality property can be used to adapt the gauge-symmetry argument of Laughlin and the topological-invariant approach of Niu, Thouless, and Wu to conditions that are much closer to real experimental ones. The resulting conclusion is that the boundary correction to the quantization of the Hall conductance is exponentially small when the system size is large compared with a microscopic length (typically the magnetic length).