Dynamics of edge currents in a linearly quenched Haldane model

Abstract

In a finite-time quantum quench of the Haldane model, the Chern number determining the topology of the bulk remains invariant, as long as the dynamics is unitary. Nonetheless, the corresponding boundary attribute, the edge current, displays interesting dynamics. For the case of sudden and adiabatic quenches the postquench edge current is solely determined by the initial and the final Hamiltonians, respectively. However for a finite-time ($\ensuremath{\tau}$) linear quench in a Haldane nanoribbon, we show that the evolution of the edge current from the sudden to the adiabatic limit is not monotonic in $\ensuremath{\tau}$ and has a turning point at a characteristic time scale $\ensuremath{\tau}={\ensuremath{\tau}}_{0}$. For small $\ensuremath{\tau}$, the excited states lead to a huge unidirectional surge in the edge current of both edges. On the other hand, in the limit of large $\ensuremath{\tau}$, the edge current saturates to its expected equilibrium ground-state value. This competition between the two limits lead to the observed nonmonotonic behavior. Interestingly, ${\ensuremath{\tau}}_{0}$ seems to depend only on the Semenoff mass and the Haldane flux. A similar dynamics for the edge current is also expected in other systems with topological phases.