Department of Physics, Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2013 May 3;110(18):180403. doi: 10.1103/PhysRevLett.110.180403. Epub 2013 May 1.
The Aubry-André or Harper (AAH) model has been the subject of extensive theoretical research in the context of quantum localization. Recently, it was shown that one-dimensional quasicrystals described by the incommensurate AAH model has a nontrivial topology. In this Letter, we show that the commensurate off-diagonal AAH model is topologically nontrivial in the gapless regime and supports zero-energy edge modes. Unlike the incommensurate case, the nontrivial topology in the off-diagonal AAH model is attributed to the topological properties of the one-dimensional Majorana chain. We discuss the feasibility of experimental observability of our predicted topological phase in the commensurate AAH model.
奥布里-安德烈或哈珀（AAH）模型一直是量子局域化背景下广泛理论研究的主题。最近，人们发现由非一致 AAH 模型描述的一维准晶具有非平凡的拓扑结构。在这封信中，我们表明，在无间隙区域，对角 AAH 模型在拓扑上是非平凡的，并支持零能边缘模式。与非一致情况不同，对角 AAH 模型中的非平凡拓扑归因于一维马约拉纳链的拓扑性质。我们讨论了在对角 AAH 模型中预测的拓扑相的实验可观测性的可行性。
