Memory-Critical Dynamical Buildup of Phonon-Dressed Majorana Fermions

TL;DR

This paper explores how non-Markovian phonon dissipation influences the dynamical behavior of Majorana fermions in a topological superconductor, revealing a transition from relaxation to buildup of Majorana correlations driven by quantum memory effects.

Contribution

It introduces the concept of memory-critical dynamical buildup of Majorana fermions in a phonon-dressed topological superconductor, highlighting the role of non-Markovian dissipation in topological state dynamics.

Findings

Majorana edge states exhibit collapse-and-buildup behavior with increasing memory depth.

A critical memory depth exists beyond which a new topological dressed state forms.

Nearly full Majorana correlation can be achieved in dynamical equilibrium with phonons.

Abstract

We investigate the dynamical interplay between topological state of matter and a non-Markovian dissipation, which gives rise to a new and crucial time scale into the system dynamics due to its quantum memory. We specifically study a one-dimensional polaronic topological superconductor with phonon-dressed $p$-wave pairing, when a fast temperature increase in surrounding phonons induces an open-system dynamics. We show that when the memory depth increases, the Majorana edge dynamics transits from relaxing monotonically to a plateau of substantial value into a collapse-and-buildup behavior, even when the polaron Hamiltonian is close to the topological phase boundary. Above a critical memory depth, the system can approach a new dressed state of topological superconductor in dynamical equilibrium with phonons, with nearly full buildup of Majorana correlation.