Edge and bulk localization of Floquet topological superconductors

Abstract

We study the bulk and edge properties of a driven Kitaev chain, where the driving is performed as instantaneous quenches of the on-site energies. We identify three periodic driving regimes: low period, which is equivalent to a static model, with renormalized parameters obtained from the Baker-Campbell-Hausdorff (BCH) expansion; intermediate period, where the first order BCH expansion breaks down; and high period when the quasienergy gap at $\omega /2$ closes. We investigate the dynamical localization properties for the case of quasiperiodic potential driving as a function of its amplitude and the pairing strength, obtaining regimes with extended, critical and localized bulk states, if the driving is performed at high frequencies. In these, we characterize wave-packet propagation, obtaining ballistic, subdiffusive and absence of spreading, respectively. In the intermediate period regime, we find an additional region in the phase diagram with a mobility edge between critical and localized states. Further, we investigate the stability of these phases under time-aperiodicity on the drivings, observing that the system eventually thermalizes: It results in featureless random states which can be described by the symmetry of the Hamiltonian. In a system with open edges, we find that both Majorana and fermionic localized edge modes can be engineered with a spatially quasiperiodic potential. Besides, we demonstrate the possibility of creating multiple Majorana $0$ and $\pi$ modes in a driven setting, even if the underlying static Hamiltonian is in its trivial phase. Lastly, we study the robustness of the Majorana modes against the aperiodicity in the driving period, showing that the ones created via quasiperiodic potential are more robust to the decoherence. Moreover, we find an example where Majorana mode is robust, provided that it is chosen from a special point in the topological region.

11+1 pages, 11+1 figures

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• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems
• Critical phase boundaries of static and periodically kicked long-range Kitaev chain
• Edge mode manipulation through commensurate multifrequency driving
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains
• Quasiperiodicity hinders ergodic Floquet eigenstates
• Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain
• Simulating Floquet topological phases in static systems
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• Topological reflection matrix
• Multifractality in monitored single-particle dynamics
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Multiple tunable real-space degeneracies in graphene irradiated by twisted light
• Family of self-dual quasicrystals with critical Phases
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain
• Noise resilience of two-dimensional Floquet topological phases