Kibble-Zurek mechanism in a topological phase transition

Abstract

The Kibble-Zurek mechanism (KZM) is generalized to a class of multilevel systems and applied to study the quenching dynamics of one-dimensional (1D) topological superconductors (TS) with open ends. Unlike the periodic boundary condition, the open boundary condition, which is crucial for the zero-mode Majorana states localized at the boundaries, requires one to consider many coupled levels. Our generalized KZM predictions agree well with the numerically exact results for the 1D TS. In particular, the generalized KZM explains well the Majorana-mode contribution to the topological defects, which utterly defies the traditional KZM. The inherent bound-state character and multilevel structure of the Majorana mode, which play key roles in the TS, are efficiently captured by the generalized KZM.