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

TL;DR

This paper investigates how Majorana edge states behave during a quantum phase transition, revealing that their dynamics are nonuniversal and depend on topological properties, with localization being key to their robustness.

Contribution

It demonstrates that Kibble-Zurek scaling does not apply to edge Majorana fermions and highlights the importance of localization for their stability during phase transitions.

Findings

Kibble-Zurek scaling fails for edge Majorana states

Edge state dynamics depend on topological features

Localization ensures robustness against defect production

Abstract

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