Emergent chiral toplogical point gaps in a non-Hermitian quasiperiodic Su-Schrieffer-Heeger model

We study a quasiperiodic Su-Schrieffer-Heeger lattice with staggered on-site gain-loss. The results reveal that on-site staggered gain-loss can effectively induce non-Hermitian topological gap without introducing imaginary phase. Further analysis exhibits that five different processes of topological phase transitions, including topological re-entrant phenomena, with the gain-loss intensity increasing. In addition, through the analysis of inverse participation ratios, normalized participation ratios, winding number and other indicators, we find that topological phase transitions occur synchronically with localized phase transitions. Finally, by investigating the properties of dual space eigenfunction, we reveal that the non-Hermitian topological point gaps predicted in this paper are chiral point gaps, which have a pair of skin modes along opposite directions simultaneously.