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We study the adiabatic dynamics of Majorana fermions across a quantum phasetransition. We show that the Kibble-Zurek scaling, which describes the densityof bulk defects produced during the critical point crossing, is not valid foredge Majorana fermions. Therefore, the dynamics governing an edge state quenchis nonuniversal and depends on the topological features of the system. Besides,we show that the localization of Majorana fermions is a necessary ingredient toguaranty robustness against defect production.

Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point