Topological Anderson insulators with different bulk states in quasiperiodic chains

We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations. In the Hermitian case, phase diagrams are obtained by numerically and analytically calculating various topological and localization characters. We show the presence of topological extended, intermediate, and localized phases due to the coexistence of independent topological and localization phase transitions driven by the quasiperiodic disorder. Unlike the gapless and localized topological Anderson insulator (TAI) phase in one-dimensional random disordered systems, we uncover three types of quasiperiodic-disorder-induced gapped TAIs with extended, intermediate (with mobility edges), and localized bulk states in this chiral chain. Moreover, we study the non-Hermitian effects on the TAIs by considering two kinds of non-Hermiticities from the nonconjugate complex hopping phase and asymmetric hopping strength, respectively. We demonstrate that three types of TAIs are preserved under the non-Hermitian perturbations with some unique localization and topological properties, such as the non-Hermitian real-complex and localization transitions and their topological nature. Our work demonstrates that the disorder-induced TAIs in Hermitian and non-Hermitian quasiperiodic systems are not tied to Anderson transitions and have various localization properties.