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

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.

11 pages, 7 figures, final version

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Topological Crystalline Insulators
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Introduction to topological superconductivity and Majorana fermions
• Epitaxy of Semiconductor-Superconductor nanowires
• Search for Majorana fermions in multiband semiconducting nanowires
• Ballistic superconductivity in semiconductor nanowires
• Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Strong localization of Majorana end states in chains of magnetic adatoms
• Topological Yu-Shiba-Rusinov chain from spin-orbit coupling
• Majorana fermions in ferromagnetic chains on the surface of bulk spin-orbit coupled $s$-wave superconductors
• Self-organized topological state in the magnetic chain on the surface of a superconductor
• Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a two-dimensional superconductor
• Topological properties of helical Shiba chains with general impurity strength and hybridization

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• Electron correlation effects in superconducting nanowires in and out of equilibrium
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• Analytical and semianalytical tools to determine the topological character of Shiba chains
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• Dynamical torques from Shiba states in $s$-wave superconductors
• Moiré dispersion of edge states in spin chains on superconductors
• RKKY interaction at helical edges of topological superconductors
• Topological phase transitions in superconductors with chiral symmetry
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Spin-dependent tunneling between individual superconducting bound states
• Magnetic ground state of supported monatomic Fe chains from first principles
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method