Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles

TL;DR

This paper investigates how controlled dissipation can stabilize degenerate steady states with Majorana modes in topological superconductors, providing theoretical insights and practical design principles.

Contribution

It establishes a theoretical framework linking equilibrium and non-equilibrium Majorana modes and proposes methods for dissipation-based stabilization in topological systems.

Findings

Derived algebraic relation between zero modes and dissipative fields.

Established correspondence between equilibrium and non-equilibrium Majorana modes.

Demonstrated framework in a long-range Kitaev chain model.

Abstract

The search for conditions supporting degenerate steady states in nonequilibrium topological superconductors is important for advancing dissipative quantum engineering, a field that has attracted significant research attention over the past decade. In this study, we address this problem by investigating topological superconductors hosting unpaired Majorana modes under the influence of environmental dissipative fields. Within the Gorini-Kossakowski-Sudarshan-Lindblad framework and the third quantization formalism, we establish a correspondence between equilibrium Majorana zero modes and non-equilibrium kinetic zero modes. We further derive a simple algebraic relation between the numbers of these excitations expressed in terms of hybridization between the single-particle wavefunctions and linear dissipative fields. Based on these findings, we propose a practical recipes how to stabilize degenerate steady states in topological superconductors through controlled dissipation engineering. To demonstrate their applicability, we implement our general framework in the BDI-class Kitaev chain with long-range hopping and pairing terms -- a system known to host a robust edge-localized Majorana modes.