Edge-state dynamics in coupled topological chains

We study time-dependent electrical properties of the Su-Schrieffer-Heeger (SSH) chain and coupled SSH chains on a substrate. Focusing on the midgap edge state dynamics we consider the abrupt transition from the normal to the SSH chain and determine characteristic timescale needed for topological states to develop. We have found that the midgap state is formed from the inside peaks of the normal chain density of states. For a ladderlike system we show that the edge SSH state vanishes in time or oscillates between neighboring sites. Moreover, for nonadiabatical time-dependent perturbations the midgap state can partially leak to other sites leading to induced topological states inside the trivial chain. We also analyze the mean-field correlation effects between the coupled chains revealing the induced Friedel oscillations in nontrivial chains.