Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain

Abstract: The interplay of topology and disorder in non-equilibrium quantum systems is an intriguing subject. Here, we look for a suitable platform that enables an in-depth exploration of the topic. To this end, We analyze the topological and localization properties of a dimerized one-dimensional Kitaev chain in the presence of an onsite quasiperiodic potential with its amplitude being modulated periodically in time. The topological features have been explored via computing the real-space winding numbers corresponding to both the Majorana zero and the $\pi$ energy modes. We enumerate the scenario at different driving frequencies. In particular, at some intermediate frequency regime, the phase diagram concerning the zero mode involves two distinct phase transitions, one from a topologically trivial to a non-trivial phase, and another from a topological phase to an Anderson localized phase. On the other hand, the study of the $\pi$ modes reveals the emergence of a unique topological phase, with the bulk and the edges being fully localized, which may be called as the Floquet topological Anderson phase. Furthermore, we study the localization properties of the bulk states by computing the inverse and normalized participation ratios, while the critical phase is ascertained by computing the fractal dimension. We have observed extended, critical, and localized phases at intermediate frequencies, which are further confirmed via a finite-size scaling analysis. Finally, fully extended and localized phases are respectively observed at lower and higher frequencies.