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Realizing Majorana modes (MMs) in condensed-matter systems is of vastexperimental and theoretical interests, and some signatures of MMs have beenmeasured already. To facilitate future experimental observations and to explorefurther applications of MMs, generating many MMs at ease in an experimentallyaccessible manner has become one important issue. This task is achieved here ina one-dimensional $p$-wave superconductor system with the nearest- andnext-nearest-neighbor interactions. In particular, a periodic modulation ofsome system parameters can induce an effective long-range interaction (assuggested by the Baker-Campbell-Hausdorff formula) and may recovertime-reversal symmetry already broken in undriven cases. By exploiting thesetwo independent mechanisms at once we have established a general method ingenerating many Floquet MMs via periodic driving.

Generating Many Majorana Modes via Periodic Driving: A Superconductor Model