Topological properties of chains of magnetic impurities on a superconducting substrate: Interplay between the Shiba band and ferromagnetic wire limits

TL;DR

This paper investigates a one-dimensional system of magnetic impurities on a superconductor, revealing how the interplay between Shiba states and conduction bands can host multiple Majorana bound states, with their stability depending on symmetry and system parameters.

Contribution

It introduces an effective low-energy Hamiltonian combining Kitaev-like models to analyze topological phases in magnetic impurity chains on superconductors.

Findings

Multiple Majorana bound states can exist at system ends with magnetic mirror symmetry.

Breaking symmetry can split Majorana states, affecting topological protection.

Phase diagram depends on exchange interactions, impurity spacing, and band coupling.

Abstract

We consider a one-dimensional system combining local magnetic moments and a delocalized metallic band on top of a superconducting substrate. This system can describe a chain of magnetic impurities with both localized polarized orbitals and delocalized s-like orbitals or a conducting wire with embedded magnetic impurities. We study the interplay between the one-dimensional Shiba band physics arising from the interplay between magnetic moments and the substrate and the delocalized wire-like conduction band on top of the superconductor. We derive an effective low-energy Hamiltonian in terms of two coupled asymmetric Kitaev-like Hamiltonians and analyze its topological properties. We have found that this system can host multiple Majorana bound states at its extremities provided a magnetic mirror symmetry is present. We compute the phase diagram of the system depending on the magnetic exchange interactions, the impurity distance and especially the coupling between both bands. In presence of inhomogeneities which typically break this magnetic mirror symmetry, we show that the coexistence of a Shiba and wire delocalized topological band can drive the system into a non-topological regime with a splitting of Majorana bound states.