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Chern insulators exhibit fascinating properties which originate from thetopologically nontrivial state characterized by the Chern number. How theseproperties change if the system is quenched between topologically distinctphases has however not been systematically explored. In this work, weinvestigate the quench dynamics of the prototypical massive Dirac model fortopological insu- lators in two dimensions. We consider both dissipation-lessdynamics and the effect of electron- phonon interactions, and ask how thetransient dynamics and nonequilibrium steady states affect simple observables.Specifically, we discuss a time-dependent generalization of the Hall effect andthe dichroism of the photoexcitation probability between left and rightcircularly polarized light. We present optimized schemes based on theseobservables, which can reveal the evolution of the topological state of thequenched system.

Tracing the nonequilibrium topological state of Chern insulators