Higher-order topological insulators and semimetals in generalized Aubry-Andr\'e-Harper models

TL;DR

This paper constructs a two-dimensional higher-order topological insulator using a generalized Aubry-Andre9-Harper model, revealing coexistence of zero and nonzero energy corner modes protected by topological invariants, and proposes an experimental realization in electric circuits.

Contribution

It introduces a generalized Aubry-Andre9-Harper model that exhibits higher-order topological phases with novel corner modes and topological protections.

Findings

Coexistence of zero-energy and nonzero-energy corner modes.

Nonzero-energy corner modes can form bound states in the continuum.

Proposed electric circuit implementation for experimental realization.

Abstract

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 non-zero 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.