Zitterbewegung And Bulk-Edge Landau-Zener Tunneling In Topological Insulators

We investigate the ballistic zitterbewegung dynamics and the Landau-Zener tunneling between edge and bulk states of wave packets in two-dimensional topological insulators. In bulk, we use the Ehrenfest theorem to show that an external in-plane electric field not only drifts the packet longitudinally, but also induces a transverse finite side jump for both trivial and topological regimes. For finite ribbons of width W, we show that the Landau-Zener tunneling between bulk and edge states vanishes for large W as their electric-field-induced coupling decays with W-3/2. This is demonstrated by expanding the time-dependent Schrodinger equation in terms of Houston states. Hence we cannot picture the quantum spin Hall states as arising from the zitterbewegung bulk trajectories "leaking" into the edge states, as proposed in Phys. Rev. B 87, 161115(R) (2013).