Dissipative topological superconductors in number-conserving systems

TL;DR

This paper explores how to engineer dissipative processes to create p-wave superconducting states in one-dimensional fermionic systems while conserving particle number, revealing different topological properties depending on the setup.

Contribution

It introduces two novel dissipative schemes for preparing number-conserving p-wave superconductors, analyzing their topological features and edge states through analytical and numerical methods.

Findings

The single wire steady state lacks topological order.

The two-leg ladder hosts Majorana zero modes at edges.

The protocols are robust and analytically tractable.

Abstract

We discuss the dissipative preparation of p-wave superconductors in number-conserving one-dimensional fermionic systems. We focus on two setups: the first one entails a single wire coupled to a bath, whereas in the second one the environment is connected to a two-leg ladder. Both settings lead to stationary states which feature the bulk properties of a p-wave superconductor, identified in this number-conserving setting through the long-distance behavior of the proper p-wave correlations. The two schemes differ in the fact that the steady state of the single wire is not characterized by topological order, whereas the two-leg ladder hosts Majorana zero modes, which are decoupled from damping and exponentially localized at the edges. Our analytical results are complemented by an extensive numerical study of the steady-state properties, of the asymptotic decay rate and of the robustness of the protocols.