Periodic Driving Induced Anomalous End Modes in a Superconducting Wire with the Second-Neighbor Pairing Potential

The anomalous end modes are generated in a one-dimensional p-wave superconducting wire with second-neighbor couplings and a periodic driving in pairing potential. We show that the driving on the amplitude or the phase of the first-neighbor and second-neighbor pairing potential can both generate conventional end modes and anomalous end modes, with corresponding Floquet eigenvalues equal to ± 1 or appear in complex conjugate pairs. We have numerically studied the driving of the first-neighbor and second-neighbor pairing potential, and also analyzed the end modes, Floquet eigenvalues and the Fourier transform of these end modes.