Topological properties of helical Shiba chains with general impurity strength and hybridization

Abstract

Recent experiments announced an observation of topological superconductivity and Majorana quasiparticles in Shiba chains, consisting of an array of magnetic atoms deposited on top of a superconductor. In this work we study helical Shiba chains and generalize the microscopic theory of subgap energy bands to a regime where the decoupled magnetic impurity energy and the hybridization of different impurity states can be significant compared to the superconducting gap of the host material. From exact solutions of the Bogoliubov-de Gennes equation we extract expressions for the topological phase boundaries for arbitrary values of the superconducting coherence length. The subgap spectral problem can be formulated as a nonlinear matrix eigenvalue problem from which we obtain an analytical solution for energy bands in the long coherence length limit. Physical consequences and departures from the previously obtained results in the deep-dilute impurity limit are discussed in detail.

arXiv comment10 pages, 8 figures

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• Topological properties of chains of magnetic impurities on a superconducting substrate: Interplay between the Shiba band and ferromagnetic wire limits
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• Superlattice platform for chiral superconductivity with tuneable and high Chern numbers
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Dynamical Shiba states by precessing magnetic moments in an s-wave superconductor
• Engineering 1D topological phases on $p$-wave superconductors
• Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator
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• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description
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• Gap inversion in one-dimensional Andreev crystals
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• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Spectral properties of Andreev crystals