Topological superconductivity in ferromagnetic atom chains beyond the deep-impurity regime

Abstract

Recent developments in the search for topological superconductivity have brought lattices of magnetic adatoms on a superconductor into intense focus. In this work we will study ferromagnetic chains of adatoms on superconducting surfaces with Rashba spin-orbit coupling. Generalising the deep-impurity approach employed extensively in previous works to arbitrary subgap energies, we formulate the theory of the subgap spectrum as a nonlinear matrix eigenvalue problem. We obtain an essentially analytical description of the subgap spectrum, allowing an efficient study of the topological properties. Employing a flat-band Hamiltonian sharing the topological properties of the chain, we evaluate the $\mathbb{Z}$-valued winding number and discover five distinct topological phases. Our results also confirm that the topological band formation does not require the decoupled Shiba energies to be fine-tuned to the gap centre. We also study the properties of Majorana bound states in the system.

11 pages, 16 figures

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Cited by in corpus (24)

• Majorana Fermions in Magnetic Chains
• Topological Phases of Inhomogeneous Superconductivity
• Topological properties of chains of magnetic impurities on a superconducting substrate: Interplay between the Shiba band and ferromagnetic wire limits
• Chern mosaic - topology of chiral superconductivity on ferromagnetic adatom lattices
• Robustness of Majorana bound states in the short junction limit
• Majorana bound state localization and energy oscillations for magnetic impurity chains on conventional superconductors
• Topological state engineering by potential impurities on chiral superconductors
• Supercurrent as a Probe for Topological Superconductivity in Magnetic Adatom Chains
• Non-Kondo many-body physics in a Majorana-based Kondo type system
• Impurity-induced excitations in a topological two-dimensional ferromagnet/superconductor van der Waals moiré heterostructure
• Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms
• Rashba induced Kondo screening of a magnetic impurity in two-dimensional superconductor
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Superlattice platform for chiral superconductivity with tuneable and high Chern numbers
• Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions
• Engineering 1D topological phases on $p$-wave superconductors
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description
• RKKY interaction at helical edges of topological superconductors
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. II. Topological classification
• Majorana Zero Modes in Ferromagnetic Wires without Spin-Orbit Coupling
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Symmetry-protected topological wire in a topological vacuum
• Spin-dependent tunneling between individual superconducting bound states