Tunable periodic cascade of delocalization transitions in non-Hermitian IAAF model

Cascade of delocalization transitions provides a route to multi-step control of delocalization, yet achieving a programmable periodic cascade remains a challenge. Here, we demonstrate a tunable periodic cascade of delocalization transitions in a non-Hermitian interpolating Aubry-André-Fibonacci (IAAF) model by introducing an imaginary phase shift into the quasiperiodic potential. Such a periodic cascade of delocalization transitions arises from the competition between kinetic-energy-facilitated delocalization and gain-loss-regulated localization. In numerical static localization characterizations, successive regular stripe patterns for localized and extended states emerge in phase diagrams. We also derive an analytical expression for the cascade period and find that it relies solely on the imaginary phase shift. This provides a direct way of continuously tuning the cascade period via a single control parameter. Complementary static and dynamical diagnostics consistently confirm this periodic cascade of delocalization transitions in the non-Hermitian IAAF system. Our findings identify a novel class of delocalization transitions with tunable cascading periods, opening a route toward experimentally programmable control of delocalization.