Topological properties of spin block magnetic ladders in proximity of a superconductor: application to BaFe$_{2}$S$_{3}$

TL;DR

This paper explores the topological phases of spin-block magnetic ladders, like BaFe$_{2}$S$_{3}$, in proximity to superconductors, revealing complex phase structures and multiple edge states relevant for Majorana modes.

Contribution

It extends the understanding of topological phases from simple chains to complex ladder structures, showing how inter-chain coupling affects topological properties and edge modes.

Findings

Coupling between chains enhances topological winding number.

Strong inter-chain coupling creates fractal-like phase diagrams.

Multiple in-gap edge states are identified and analyzed.

Abstract

Monoatomic chains with magnetic order in proximity of a s-wave superconductor can host Majorana edge modes. In this paper, we extend this idea to more complex spin-block chains such as the BaFe$_{2}$S$_{3}$ magnetic material that has a spin-ladder like structure. We investigate the topological phase diagram of such a system as function of the system parameters. We show that the coupling between chains within the ladder leads to the topological phase with a winding number larger than the sum of two single magnetic chains. Furthermore, strong coupling between chains leads to fractal-like substructure in the topological phase diagram. By investigating the real space properties of such a system and particularly its edge modes, we find that the system spectrum contains several in-gap states that we analyze in detail.