Band topology and Bloch oscillation in an extended Creutz ladder

Abstract

We study an extended Creutz ladder system, which supports topological phase transition as revealed by the change of topological invariant and by distinct pseudospin textures. With a linear force along the ladder, Bloch oscillation on topological bands is studied. At the topological phase transition point, the oscillation period is doubled due to band crossings and the wave packet evolves alternatively on the two bands. The magnitude of pseudospin polarizations in Bloch oscillation provide a dynamical identification of the topological feature. The local pseudospin polarizations along y − and z − axis are directly related to measurable inter-leg current and density difference. We also show the micromotion and non-adiabatic propagations of the Bloch wave packet. A small density oscillation beyond the description of Bloch oscillation is revealed. At avoided band crossings, the transition probability of the Landau-Zener tunneling is obtained. Our results exhibit a transparent framework to understand the properties of topological bands and of Bloch wave dynamics.