Zitterbewegung and Bulk-Edge Landau-Zener Tunneling in 2D Topological Insulators

We investigate the ballistic dynamics and the Landau-Zener tunneling between edge and bulk states in 2D 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 trembling motion (Zitterbewegung) and a transverse side-jump, whose direction, although dependent on the gap sign, is finite for both the trivial and nontrivial topological regimes. For finite ribbons of width W, we show that the Landau-Zener tunneling between bulk and edge states vanish for large W as their electric field induced coupling decays with W^-3/2. This is demonstrated by expanding the time-dependent Schrödinger equation in terms of Houston states. We conclude that, contrary to what has been proposed, we cannot picture the quantum spin Hall states as arising from Zitterbewegung bulk trajectories ‘leaking’ into the edge states.