Bloch Oscillations

What you are seeing: a particle in a 1D cosine band, driven by a uniform force $F$ . Quasi-momentum slides through the Brillouin zone at constant rate; group velocity flips sign at the zone boundary, and the position oscillates with period $T_B = h / (eFa)$ .

Figure 1. Band

E(k)

(top), particle position

x(t)

(bottom).

F (force)1.00

W (bandwidth)1.00

WHAT TO TRY

Apply the force F: the quasi-momentum sweeps through the Brillouin zone at a constant rate and the group velocity flips sign at the zone edge, so the particle oscillates rather than running away. That is a Bloch oscillation.
The period T_B = h / (F a) shrinks as you push harder: a steady force gives periodic motion, the counterintuitive result that a DC field drives an AC current in a perfect lattice.
Narrow the bandwidth W: the oscillation amplitude shrinks, since the particle only roams as far as the band is wide before the zone edge turns it around.