Single and multifrequency driving protocols in a Rashba nanowire proximitized to an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi></mml:math>-wave superconductor

We perform systematic analyses of single and multifrequency driving protocols on a Rashba nanowire with superconducting correlations induced by proximity effects. The results for the single-mode drive reveal interesting frequency dependencies of the Majorana modes, in the sense that the parameters corresponding to the trivial and the topological limits of the undriven (static) case host Majorana zero modes, respectively, at low and high frequencies. Further, emergence of long-range interactions are noted that give rise to multiple gap-closing scenarios, where the latter implies occurrence of multiple Majorana modes. On the other hand, the multifrequency driving protocol, subgrouped into commensurate and incommensurate ratios of the frequencies, demonstrates intriguing consequences. The commensurate case yields dynamical control over the stability of the edge modes, whereas more intricate driving protocols, such as those with larger frequency ratios, are studies as well and they are found to harm the Majoranas by pushing them into the bulk. Finally, the incommensurate case yields independent Majorana modes occurring at low-symmetry points in the Brillouin zone. While the single and the commensurate multifrequency driving protocols admit the usage of symmetric time frames for the computation of the topological invariants, the incommensurate case relies on the framework of many-mode Floquet theory, where the topological properties are ascertained via calculating the Berry phase. We present band structure and phase diagrams to substantiate all our results. The robustness and concurrent existence of these unique Majorana modes, even amid a very dense energy spectrum along with a lack of global time periodicity, hold promise for future applications in the field of quantum computation.