End states and subgap structure in proximity-coupled chains of magnetic adatoms

Abstract

A recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] provides evidence for Majorana zero modes in iron (Fe) chains on the superconducting Pb(110) surface. Here, we study this system by scanning tunneling microscopy using superconducting tips. This high-resolution technique resolves a rich subgap structure, including zero-energy excitations in some chains. We compare the symmetry properties of the data under voltage reversal against theoretical expectations and provide evidence that the putative Majorana signature overlaps with a previously unresolved low-energy resonance. Interpreting the data within a Majorana framework suggests that the topological gap is significantly smaller than previously believed. Aided by model calculations, we also analyze higher-energy features of the subgap spectrum and their relation to high-bias peaks which we associate with the Fe d-bands.

5+5 pages, 5+6 figures

References in corpus (15)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Edge-mode Superconductivity in a Two Dimensional Topological Insulator
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Tunneling processes into localized subgap states in superconductors
• Strong localization of Majorana end states in chains of magnetic adatoms
• Protection of excited spin states by a superconducting energy gap
• Topological Yu-Shiba-Rusinov chain from spin-orbit coupling
• Experimental demonstration of a two-band superconducting state for lead using scanning tunneling spectroscopy
• Bound states of a ferromagnetic wire in a superconductor

Cited by in corpus (276)

• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Probing Atomic Structure and Majorana Wavefunctions in Mono-Atomic Fe-chains on Superconducting Pb-Surface
• Distinguishing a Majorana zero mode using spin resolved measurements
• Two-dimensional platform for networks of Majorana bound states
• High-resolution studies of the Majorana atomic chain platform
• Two-dimensional topological superconductivity in Pb/Co/Si(111)
• Single magnetic adsorbates on s-wave superconductors
• Signature of Dispersing 1D Majorana Channels in an Iron-based Superconductor
• Colloquium: Atomic spin chains on surfaces
• Atomic-Scale Interface Engineering of Majorana Edge Modes in a 2D Magnet-Superconductor Hybrid System
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Disorder-induced zero-bias peaks in Majorana nanowires
• Exploring a proximity-coupled Co chain on Pb(110) as a possible Majorana platform
• Magnetic anisotropy in Shiba bound states across a quantum phase transition
• Tuning the coupling of an individual magnetic impurity to a superconductor: quantum phase transition and transport
• Orbital Picture of Yu-Shiba-Rusinov Multiplets
• Effects of gate-induced electric fields on semiconductor Majorana nanowires
• Coupled Yu-Shiba-Rusinov states in molecular dimers on NbSe${}_2$
• Evidence of topological Shiba bands in artificial spin chains on superconductors
• Mapping the orbital structure of impurity bound states in a superconductor
• Controlled length-dependent interaction of Majorana modes in Yu-Shiba-Rusinov chains
• Majorana nanowires for topological quantum computation
• Low-energy theory of transport in Majorana wire junctions
• Metallization of Rashba wire by superconducting layer in the strong-proximity regime
• Hunting for Majoranas
• Wave-function hybridization in Yu-Shiba-Rusinov dimers
• Observation of Coexistence of Yu-Shiba-Rusinov States and Spin-Flip Excitations
• Proximity-induced Majorana hinge modes in antiferromagnetic topological insulators
• Self-Organized Topological Superconductivity in a Yu-Shiba-Rusinov Chain
• Probing magnetic interactions between Cr adatoms on the $\beta$-Bi${}_2$Pd superconductor
• Signatures of topological Josephson junctions
• Dirac, Rashba and Weyl type spin-orbit couplings: toward experimental realization in ultracold atoms
• Amorphous topological superconductivity in a Shiba glass
• Topological Superconductivity in Skyrmion Lattices
• Engineering the spin couplings in atomically crafted spin chains on an elemental superconductor
• Spin-dependent coupling between quantum dots and topological quantum wires
• Weak measurement protocols for Majorana bound state identification
• Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime
• Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
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• Controlling in-gap end states by linking nonmagnetic atoms and artificially-constructed spin chains on superconductors
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• Quantized charge transport in chiral Majorana edge modes
• Majorana Fermions in Magnetic Chains
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• Majorana bound states in semiconducting nanostructures
• Topological Phase Detection in Rashba Nanowires with a Quantum Dot
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• Braiding Majorana zero modes using quantum dots
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• Observation of tunable single-atom Yu-Shiba-Rusinov states
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• Gap Anisotropy in Multiband Superconductors Based on Multiple Scattering Theory
• Proximity effect in a two-dimensional electron gas coupled to a thin superconducting layer
• Localization-enhanced and degraded topological-order in interacting p-wave wires
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• Degeneracy lifting of Majorana bound states due to electron-phonon interactions
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• Asymptotic behavior of impurity-induced bound states in low-dimensional topological superconductors
• Quantum Engineering of Majorana Fermions
• Robustness of Yu-Shiba-Rusinov resonances in presence of a complex superconducting order parameter
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• Coherent and incoherent tunneling into YSR states revealed by atomic scale shot-noise spectroscopy
• Effects of the electrostatic environment on superlattice Majorana nanowires
• Tunneling processes between Yu-Shiba-Rusinov bound states
• Prevalence of trivial zero-energy sub-gap states in non-uniform helical spin chains on the surface of superconductors
• Superconducting order parameter $\pi$-phase shift in magnetic impurity wires
• Identification of Majorana Modes in Interacting Systems by Local Integrals of Motion
• Majorana fermions at odd junctions in a wire network of ferromagnetic impurities
• Topological state engineering by potential impurities on chiral superconductors
• Testing the topological nature of end states in antiferromagnetic atomic chains on superconductors
• Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions
• Magnetic impurities in spin-split superconductors
• Dynamics of hybrid junctions of Majorana wires
• Realizing Topological Superconductivity with Superlattices
• Topological superconductivity in EuS/Au/superconductor heterostructures
• Topological $\pi$-junctions from crossed Andreev reflection in the Quantum Hall regime
• Parafermionic generalization of the topological Kondo effect
• Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving $s$-wave one-dimensional superconductors
• Josephson effect in junctions of conventional and topological superconductors
• Controlling topological superconductivity by magnetization dynamics
• Yu-Shiba-Rusinov bound states induced by a spin flipper in the vicinity of a s-wave superconductor
• Detecting coupling of Majorana bound states with an Aharonov-Bohm interferometer
• Majorana quasiparticles in atomic spin chains on superconductors
• Single-electron charge transfer into putative Majorana and trivial modes in individual vortices
• Origin of Topological Surface Superconductivity in FeSe${}_{0.45}$Te${}_{0.55}$
• Rashba Sandwiches with Topological Superconducting Phases
• Electron waiting times in hybrid junctions with topological superconductors
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• Collective Yu-Shiba-Rusinov states in magnetic clusters at superconducting surfaces
• Fermi liquid approach for superconducting Kondo problems
• Majorana bound state engineering via efficient real-space parameter optimization
• Analytic approach to transport in superconducting junctions with arbitrary carrier density
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Yu-Shiba-Rusinov states in 2D superconductors with arbitrary Fermi contours
• Supercurrent as a Probe for Topological Superconductivity in Magnetic Adatom Chains
• Majorana zero modes and their bosonization
• Hierarchical Majoranas in a Programmable Nanowire Network
• Magnetic manipulation of topological states in p-wave superconductors
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Non-Kondo many-body physics in a Majorana-based Kondo type system
• Engineering of Chern insulators and circuits of topological edge states
• Majorana bound states in nanowire-superconductor hybrid systems in periodic magnetic fields
• Stability of Disordered Topological Superconducting Phases in Magnet--Superconductor Hybrid Systems
• Odd-frequency superconductivity in dilute magnetic superconductors
• Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors
• Quasiperiodic criticality and spin-triplet superconductivity in superconductor-antiferromagnet moire patterns
• Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Trapping Majorana Zero Modes in Vortices of Magnetic Texture Crystals Coupled to Nodal Superconductors
• Quasiparticle focusing of bound states in two-dimensional $s$-wave superconductors
• Nodal S-wave Superconductivity in Antiferromagnetic Semimetals
• First principles study of topological phase in chains of $3d$ transition metals
• Yu-Shiba-Rusinov States and Ordering of Magnetic Impurities Near the Boundary of a Superconducting Nanowire
• Moving Majorana bound states between distinct helical edges across a quantum point contact
• Hamiltonian learning with real-space impurity tomography in topological moire superconductors
• Full Counting Statistics of Yu-Shiba-Rusinov Bound States
• Spin-orbital polarization of Majorana edge states in oxides nanowires
• Time-Reversal Invariant Topological Superconductivity in Planar Josephson Bijunction
• Search for large topological gaps in atomic spin chains on proximitized superconducting heavy metal layers
• Quantum transport in coupled Majorana box systems
• Topologically nontrivial and trivial zero modes in chiral molecules
• Quantum engineering of Majorana quasiparticles in one-dimensional optical lattices
• Increased localization of Majorana modes in antiferromagnetic chains on superconductors
• Driving Topological Phases by Spatially Inhomogeneous Pairing Centers
• Transport signatures of topological phases in double nanowires probed by spin-polarized STM
• Coherent coupling between vortex bound states and magnetic impurities in 2D layered superconductors
• Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms
• Concomitant opening of a topological bulk-gap with an emerging Majorana edge-state
• Interaction Driven Floquet Engineering of Topological Superconductivity in Rashba Nanowires
• Interaction-induced topological superconductivity in antiferromagnet-superconductor junctions
• Tunable topological states hosted by unconventional superconductors with adatoms
• Effect of Van Hove singularities on Shiba states in two-dimensional $s$-wave superconductors
• Majorana zero modes by engineering topological kink states in two dimensional electron gas
• Holonomic implementation of CNOT gate on topological Majorana qubits
• Rashba induced Kondo screening of a magnetic impurity in two-dimensional superconductor
• Voltage-tunable Majorana bound states in time-reversal symmetric bilayer quantum spin Hall hybrid systems
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Gap oscillations and Majorana bound states in magnetic chains on superconducting honeycomb lattices
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Spin-fluctuation and spin-relaxation effects of single adatoms from first principles
• Superlattice platform for chiral superconductivity with tuneable and high Chern numbers
• Constrained thermalisation and topological superconductivity
• Proximity-Induced Superconductivity in Atomically Precise Nanographene
• Fano resonances can provide two criteria to distinguish Majorana bound states from other candidates in experiments
• Majorana Zero Modes in Cylindrical Semiconductor Quantum Wire
• An atomically thin oxide layer on the elemental superconductor Ta(001) surface
• Quantum charge pumping through Majorana bound states
• Scanning tunneling spectroscopy investigations of superconducting-doped topological insulators: Experimental pitfalls and results
• Dynamical Shiba states by precessing magnetic moments in an s-wave superconductor
• Majorana-magnon interactions in topological Shiba chains
• Impurity-induced subgap states in superconductors with inhomogeneous pairing
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Dynamical torques from Shiba states in $s$-wave superconductors
• Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description
• Grain-boundary topological superconductor
• Topological superconductivity in proximity to type-II superconductors
• Topological Transitions in a Model for Proximity Induced Superconductivity
• RKKY interaction at helical edges of topological superconductors
• Simulating spin systems with Majorana networks
• Quantum phase diagram of Shiba impurities from bosonization
• Probing Magnetic and Triplet Correlations in Spin-Split Superconductors with Magnetic Impurities
• Influence of Rashba spin-orbit coupling on the 0-$\pi$ transition and Kondo temperature in 1D superconductors
• Gate-tunable topological superconductivity in a supramolecular electron spin lattice
• Magnetic impurities on superconducting Pb surfaces
• Effects of nonmagnetic disorder on the energy of Yu-Shiba-Rusinov states
• Effects of electron-electron interactions in the Yu-Shiba-Rusinov lattice model
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Superconducting quantum dot and the sub-gap states
• Spin-resolved nonlocal transport in proximitized Rashba nanowires
• Anisotropy and spin-fluctuation effects on the spectral properties of Shiba impurities
• Topological superconductivity driven by correlations and linear defects in multiband superconductors
• Investigation of the Yu-Shiba-Rusinov states of a multi-impurity Kondo system
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Fractionalization of Majorana-Ising-type quasiparticles
• Constructing edge zero modes through domain wall angle conservation
• Interplay between pairing and correlations in spin-polarized bound states
• Band twisting and resilience to disorder in long-range topological superconductors
• Non-Abelian operation through scattering between chiral Dirac edge modes
• Anomalous superconducting proximity effect of planar Pb-RhPb2 heterojunctions in the clean limit
• Renormalization effects in spin-polarized metallic wires proximitized by a superconductor: A scattering approach
• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Embedded Majorana Islands
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Temperature dependent energy gap for Yu-Shiba-Rusinov states at the quantum phase transition
• Subgap states and quantum phase transitions in one-dimensional superconductor-ferromagnetic insulator heterostructures
• Odd-parity ground state in dilute Yu-Shiba-Rusinov dimers and chains
• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions
• Fermi-Level Pinning of Yu-Shiba-Rusinov States in a Superconductor with Weakly Broken Spin-Rotational Invariance
• Cooper Pair Induced Frustration and Nematicity of Two-Dimensional Magnetic Adatom Lattices
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Direct signatures of $d$-level hybridization and dimerization in magnetic adatom chains on a superconductor
• Realistic indirect spin-interactions between magnetic impurities on a metallic Pb(110) surface
• Yu-Shiba-Rusinov bound states boost odd-frequency superconductivity
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Symmetry-protected topological wire in a topological vacuum
• Dimensional crossover of class D real-space topological invariants
• Detecting and Distinguishing Majorana Zero Modes with the Scanning Tunneling Microscope
• Field-free Superconducting Diode Effect and Topological Fulde-Ferrell Superconductivity in Altermagnetic Shiba Chains
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems