Slow quenches in Chern insulator ribbons

Abstract

We investigate slow quenches in Chern insulators in ribbon geometry. We consider the Qi-Wu-Zhang model and slowly ramp the parameters (large time of the quench $\ensuremath{\tau}$) from a nontopological (Chern number = 0) to a topological regime (Chern number $\ensuremath{\ne}$ 0). In contrast to the Haldane model considered in [L. Privitera and G. E. Santoro, Phys. Rev. B 93, 241406(R) (2016)], the in-gap state degeneracy point is pinned to an inversion symmetric momentum, which changes the behavior drastically. The density of excitations in the in-gap states scales with the quench time as ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ as the ramp becomes slow, and the Kibble-Zurek mechanism applies. Despite the slower scaling of the density of in-gap excitations with $\ensuremath{\tau}$, the Hall conductance after the quench deviates from that of the ground state of the final Hamiltonian by an amount that drops as ${\ensuremath{\tau}}^{\ensuremath{-}1}$.