Dissipation induced Majarona $0$- and $\pi$-modes in a driven Rashba nanowire

TL;DR

This paper explores how dissipation influences topological Majorana modes in a periodically driven Rashba nanowire, revealing the emergence of both topological and trivial edge modes and their robustness against disorder.

Contribution

It introduces a framework using the Liouvillian operator and third-quantization to analyze dissipative driven topological systems, identifying new trivial edge modes and the impact of dissipation on topological phases.

Findings

Edge-localized Majorana 0- and π-modes are realized in the system.

Dissipation can induce and modify topological phases.

Trivial edge modes are also present and are tied to exceptional points.

Abstract

Periodic drive is an intriguing way of creating topological phases in a non-topological setup. However, most systems are often studied as a closed system, despite being always in contact with the environment, which induces dissipation. Here, we investigate a periodically driven Rashba nanowire in proximity to an $s$-wave superconductor in a dissipative background. The system's dynamics is governed by a periodic Liouvillian operator, from which we construct the Liouvillian time-evolution operator and use the third-quantization method to obtain the `Floquet damping matrix', which captures the spectral and topological properties of the system. We show that the system exhibits edge-localized topological Majorana $0$-modes (MZMs) and $\pi$-modes (MPMs). Additionally, the system also supports a trivial $0$-modes (TZMs) and $\pi$-modes (TPMs), which are also localized at the edges of the system. The MZMs and the MPMs are connected to the bulk topology and carry a bulk topological invariant, while the emergence of TZMs and TPMs is primarily tied to exceptional points and is topologically trivial. We show that both the topological (MZMs and MPMs) and trivial (TZMs and TPMs) edge modes are robust against onsite disorder. We study the topological phase diagrams in terms of the topological invariants and show that the dissipation can modify the topological phase diagram substantially and even induce topological phases in the system. Our work extends the understanding of a driven-dissipative topological superconductor.