Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models

• Published in: Physical review. B 2020-06, Vol.101 (24), p.1, Article 241104
• Main Authors: Zeng, Qi-Bo, Yang, Yan-Bin, Xu, Yong
• Format: Article
• Language: English
• Subjects: Circuits; Metalloids; Phases; Quadrupoles; Topological insulators; Topology; Two dimensional models
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.101.241104

Higher-order topological phases of matter have been extensively studied in various areas of physics. While the Aubry-André-Harper model provides a paradigmatic example to study topological phases, it has not been explored whether a generalized Aubry-André-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-André-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-André-Harper model.