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Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice
Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2021-08-16 , DOI: 10.1007/s00023-021-01097-2
Alex Bols 1 , Albert H. Werner 1, 2
Affiliation  

The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single-particle picture, be supported in the absolutely continuous spectrum of the single-particle Hamiltonian. We show in this note that if a free fermion system on the two-dimensional lattice is gapped in the bulk and has a non-vanishing Hall conductance, then the same system put on a half-space geometry supports edge modes whose spectrum fills the entire bulk gap and is absolutely continuous.



中文翻译:

晶格上霍尔绝缘体的绝对连续边缘谱

量子霍尔样品边缘手征模式的存在对于我们理解量子霍尔效应至关重要。特别是,这些边缘模式应该支持弹道传输,因此,在单粒子图片中,在单粒子哈密顿量的绝对连续谱中得到支持。我们在这篇笔记中表明,如果二维晶格上的自由费米子系统在体中存在间隙并且具有非零霍尔电导,那么置于半空间几何结构上的同一系统支持边缘模式,其光谱填充整个大块间隙并且是绝对连续的。

更新日期:2021-08-19
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