Quenching in Chern insulators with satellite Dirac points: The fate of edge states

We perform a sudden quench on the Haldane model with long range interactions, more specifically generalizing to the next to next nearest neighbor hopping, referred to as the N3 model in our work. Such a model possesses both isotropic and multiple anisotropic (satellite) Dirac points which lead to a rich topological phase diagram consisting of phases with higher Chern number (C). Quenches between the topological and the nontopological phases of such an infinite system probe the effect of the presence of the anisotropic Dirac points on the nonequilibrium response of the topological system. Interestingly, the Chern number remains the same before and after the quench for both the quenching protocols, even when the quench of the system is carried out between two different topological phases. However, for a finite system, we establish that the initial edge current asymptotically decays to zero when the system is quenched to the nontopological phase although the Chern number for the corresponding periodically wrapped system remains unaltered; what is remarkable is that when the Hamiltonian is quenched from vertical bar C vertical bar = 2 phase to the nontopological phase the edge current associated with the inner channel decays at a faster rate than the outer channel resembling a situation in which the system passes through the phase with vertical bar C vertical bar = 1 before ending up in the phase C = 0.