Strong localization of Majorana end states in chains of magnetic adatoms

Abstract

A recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] gives possible evidence for Majorana bound states in chains of magnetic adatoms placed on a superconductor. While many features of the observed end states are naturally interpreted in terms of Majoranas, their strong localization remained puzzling. We consider a linear chain of Anderson impurities on a superconductor as a minimal model and treat it largely analytically within mean-field theory. We explore the phase diagram, the subgap excitation spectrum, and the Majorana wavefunctions. Owing to a strong velocity renormalization, the latter are localized on a scale which is parametrically small compared to the coherence length of the host superconductor.

to appear in PRL; includes new heuristic section; 5 pages + supplementary material

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Cited by in corpus (66)

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• Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model
• Controlled length-dependent interaction of Majorana modes in Yu-Shiba-Rusinov chains
• Majorana nanowires for topological quantum computation
• Hunting for Majoranas
• Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime
• Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a two-dimensional superconductor
• Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor
• Majorana Fermions in Magnetic Chains
• Yu-Shiba-Rusinov states in real metals
• Topological properties of chains of magnetic impurities on a superconducting substrate: Interplay between the Shiba band and ferromagnetic wire limits
• Yu-Shiba-Rusinov qubit
• Majorana modes in emergent-wire phases of helical and cycloidal magnet-superconductor hybrids
• Majorana Bound States Induced by Antiferromagnetic Skyrmion Textures
• Robustness of Majorana bound states in the short junction limit
• Aspects of topological superconductivity in 2D systems: noncollinear magnetism, skyrmions, and higher-order topology
• Atomic Manipulation of In-gap States on the $\beta$-Bi${}_2$Pd Superconductor
• DIII Topological Superconductivity with Emergent Time-Reversal Symmetry
• Quantum magnetism and topological superconductivity in Yu-Shiba-Rusinov chains
• Majorana quasiparticles of inhomogeneous Rashba chain
• Identifying Majorana bound states by tunneling shot-noise tomography
• Coupling of Yu-Shiba-Rusinov states in 1D chains of Fe atoms on Nb(110)
• Topological superconductivity in carbon nanotubes with a small magnetic flux
• Prevalence of trivial zero-energy sub-gap states in non-uniform helical spin chains on the surface of superconductors
• Testing the topological nature of end states in antiferromagnetic atomic chains on superconductors
• Realizing Topological Superconductivity with Superlattices
• Topological superconductivity in EuS/Au/superconductor heterostructures
• Majorana quasiparticles in atomic spin chains on superconductors
• Majorana states and magnetic orbital motion in planar hybrid nanowires
• Probing Majorana-like states in quantum dots and quantum rings
• Substrate-induced Majorana renormalization in topological nanowires
• Closing the superconducting gap in small Pb-nanoislands with high magnetic fields
• Theory of Coulomb blockaded transport in realistic Majorana nanowires
• Topological superconductivity at finite temperatures in proximitized magnetic nanowires
• Influence of long-range interaction on Majorana zero modes
• Chemical Principles of Intrinsic Topological Superconductors
• Yu-Shiba-Rusinov states in 2D superconductors with arbitrary Fermi contours
• Renormalization of the Majorana bound state decay length in a perpendicular magnetic field
• Majorana phase-gate based on the geometric phase
• Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors
• Majorana end states in an interacting quantum wire
• Do Majorana zero modes emerge in the hybrid nanowire under a strong magnetic field?
• Observation of Yu-Shiba-Rusinov-like states at the edge of CrBr3/NbSe2 heterostructure
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Dynamical torques from Shiba states in $s$-wave superconductors
• Spin-polarized currents and noise in NS junctions with Yu-Shiba-Rusinov impurities
• Optically and electrically controllable adatom spin-orbital dynamics in transition metal dichalcogenides
• Platform for controllable Majorana zero modes using superconductor/ferromagnet heterostructures
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. II. Topological classification
• RKKY interaction at helical edges of topological superconductors
• Moiré dispersion of edge states in spin chains on superconductors
• Topological superconductivity in proximity to type-II superconductors
• Majorana Zero Modes in Ferromagnetic Wires without Spin-Orbit Coupling
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Subgap modes in two-dimensional magnetic Josephson junctions
• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method
• Scanning tunneling microscopy study of helimagnetic monolayer CrBr2 on s-wave superconductor NbSe2: a topologically trivial system due to weak interfacial coupling
• Time-reversal symmetric topological superconductivity in Machida-Shibata lattices
• Symmetry-protected topological wire in a topological vacuum
• Detecting and Distinguishing Majorana Zero Modes with the Scanning Tunneling Microscope