Dynamics of edge current in a linearly quenched Haldane model

TL;DR

This paper investigates how the edge current in a Haldane model nano ribbon evolves during a finite time linear quench, revealing a non-monotonic behavior with a characteristic time scale influenced by system parameters.

Contribution

It uncovers the non-monotonic dynamics of edge current during a linear quench in the Haldane model and identifies the dependence of the critical time on system parameters.

Findings

Edge current shows non-monotonic behavior during linear quench.

A characteristic time scale $ au_c$ influences the edge current dynamics.

Large $ au$ leads to saturation of edge current to equilibrium value.

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 post quench edge current is solely determined by the initial and the final Hamiltonians, respectively. However for a finite time ($\tau$) linear quench in a Haldane nano ribbon, we show that the evolution of the edge current from the sudden to the adiabatic limit is not monotonic in $\tau$, and has a turning point at a characteristic time scale $\tau=\tau_c$. For small $\tau$, the excited states lead to a huge unidirectional surge in the edge current of both the edges. On the other hand, in the limit of large $\tau$, the edge current saturates to its expected equilibrium ground state value. This competition between the two limits lead to the observed non-monotonic behavior. Interestingly, $\tau_c$ 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.