Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
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DOI：
10.1103/physrevb.101.241104
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发表时间：
2020-06
影响因子：
3.7
通讯作者：
Q. Zeng;Yan-Bin Yang;Yong Xu
中科院分区：
文献类型：
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作者：
Q. Zeng;Yan-Bin Yang;Yong Xu
物质的高阶拓扑相在物理学的各个领域都得到了广泛的研究。虽然Aubry-Andr\'e-Harper模型提供了一个研究拓扑相的范例，但还没有探索广义Aubry-Andr\' e-Harper模型是否可以表现出高阶拓扑现象。本文基于Aubry-Andr\'e-Harper模型构造了一个具有手征对称性的二维高阶拓扑绝缘体.我们发现零能和非零能角局域模共存。前者受到量子化四极矩的保护，而后者受到Wannier带的第一Chern数的保护。非零能量模式也可以被看作是一个陈绝缘体定位在一个表面上的结果。更有趣的是，非零能量角模可以位于扩展体态的连续体中，并在高阶拓扑系统的连续体中形成束缚态。最后，我们提出了一个实验方案，以实现我们的模型在电路中。我们的研究为进一步研究基于Aubry-Andr\'e-Harper模型的高阶拓扑相打开了一扇大门。
Higher-order topological phases of matter have been extensively studied in various areas of physics. While the Aubry-Andr\'e-Harper model provides a paradigmatic example to study topological phases, it has not been explored whether a generalized Aubry-Andr\'e-Harper model can exhibit a higher-order topological phenomenon. Here, we construct a two-dimensional higher-order topological insulator with chiral symmetry based on the Aubry-Andr\'e-Harper model. We find the coexistence of zero-energy and nonzero-energy corner-localized modes. The former is protected by the quantized quadrupole moment, while the latter by the first Chern number of the Wannier band. The nonzero-energy mode can also be viewed as the consequence of a Chern insulator localized on a surface. More interestingly, the nonzero-energy corner mode can lie in the continuum of extended bulk states and form a bound state in the continuum of higher-order topological systems. We finally propose an experimental scheme to realize our model in electric circuits. Our study opens a door to further study higher-order topological phases based on the Aubry-Andr\'e-Harper model.