Wave packet dynamics under superposed DC and AC fields: Super Bloch oscillations, resonant directed motion and delocalization

We investigate the wave packet dynamics of an electron restricted to a periodic one-dimensional lattice and driven by an external field having both DC and AC components. We show that when the frequency of the AC field is a multiple of the frequency of the usual Bloch oscillations, a directed motion of the wave packet is promoted whose average velocity depends on the magnitudes of the AC and DC field components and on the initial phase of the AC field. Super Bloch oscillations and breathing take place with an amplitude that diverges as the resonance condition is approached. ► We study the influence of the superposition of an AC and DC field in the wave packet dynamic. ► Direct motion of the wave packet can be achieved depending on AC field frequency and initial phase. ► Super Bloch oscillation and breathing take place when the AC frequency is not in the resonance.