Edge mode manipulation through commensurate multifrequency driving

Abstract

We explore the impact of commensurate multifrequency driving protocols on the stability of topological edge modes in topological 1D systems of spinless fermions. Using Floquet theory, we show that all the topological phase transitions can be mapped to their single-frequency counterparts in terms of effective driving parameters. This drastic simplification can be explained by considering the gap closures in the quasienergy dispersion. These gap closures are pinned to high-symmetry points, where all the effective Floquet Hamiltonians collapse to the same form. While for all protocols all topological phase transitions coincide, the gap size and the number of edge modes in the quasienergy spectra vary considerably depending on the chosen driving pattern. This gives rise to a full range of edge states with different degrees of localization, from highly localized to completely delocalized. Switching between different driving protocols then suggests a dynamical control of the localization and stability of topological edge modes, with possible applications in quantum computation. We illustrate our findings on three paradigmatic fermionic systems -- namely the Kitaev chain, the Su-Schrieffer-Heeger model, and the Creutz ladder, and demonstrate how to control the localization length of the corresponding edge states.

16 pages, 15 figures

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• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain
• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Topological phase transition in commensurate multi-frequency Floquet Su-Schrieffer-Heeger model
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Emerging topological characterization in non-equilibrium states of quenched Kitaev chains
• Tunable zero modes and quantum interferences in flat-band topological insulators