Chern insulators exhibit fascinating properties which originate from the topologically nontrivial state characterized by the Chern number. How these properties are affected and manifest in the presence time-dependent perturbations is still a sparsely explored field of research. This applies,in particular, to quantum quenches between topologically distinct phases. Identifying robust measures of topology which are applicable in nonequilibrium scenarios — ideally also for correlated materials or dissipative systems — is thus a nontrivial task.
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