Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor

Abstract

Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero energy end states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains.

18 pages, 5 figures, and supplementary information. appears in Science (2014)

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• Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states
• Effect of Van Hove singularities on Shiba states in two-dimensional $s$-wave superconductors
• Majorana excitons in a Kitaev chain of semiconductor quantum dots in a nanowire
• Interaction-induced topological superconductivity in antiferromagnet-superconductor junctions
• Tunable topological states hosted by unconventional superconductors with adatoms
• Diagnosing Topological Phase Transitions in 1D Superconductors using Berry Singularity Markers
• Finite temperature effects on Majorana bound states in chiral $p$-wave superconductors
• Diamagnetic property and optical absorption in conventional superconductors with magnetic impurities
• The quest and hope of Majorana zero modes in topological superconductor for fault-tolerant quantum computing: an introductory overview
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Stacking-Induced Symmetry-Protected Topological Phase Transitions
• Electronic correlations effect on nontrivial topological fermions in CoSi
• Molecular beam epitaxy of superconducting Sn${}_{1-x}$In${}_x$Te thin films
• Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors
• Proximity-Induced Superconductivity in Atomically Precise Nanographene
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Superlattice platform for chiral superconductivity with tuneable and high Chern numbers
• An odd-frequency Cooper pair around a magnetic impurity
• Quantum phase transition in magnetic nanographenes on a lead superconductor
• Reduced quantum electrodynamics in curved space
• Yu-Shiba-Rusinov states in a superconductor with topological Z2 bands
• Topological multiband s-wave superconductivity in coupled multifold fermions
• Quasiparticle Interference Patterns in a Topological Superconductor
• Transport in topological insulator nanowires
• Dynamical approach to improving Majorana qubits and distinguishing them from trivial bound states
• Chiral topological superconducting state with Chern number $\mathcal{C}=-2$ in Pb${}_3$Bi/Ge(111)
• Noncentrosymmetric superconductors in one dimension
• Entangled states of two quantum dots mediated by Majorana fermions
• Superconductivity in quantum wires: A symmetry analysis
• Weyl points in systems of multiple semiconductor-superconductor quantum dots
• Magnetoelectric Response in Electric Octupole State: Possible Hidden Order in Cuprate Superconductors
• Observation of Persistent Zero Modes and Superconducting Vortex Doublets in UTe${}_2$
• Current Flow in Topological Insulator Josephson Junctions due to Imperfections
• Multicritical quantum sensors driven by symmetry-breaking
• Wannier center spectroscopy to identify boundary-obstructed topological insulators
• Quantum spin driven Yu-Shiba-Rusinov multiplets and fermion-parity-preserving phase transition in K${}_3$C${}_{60}$
• Majorana-magnon interactions in topological Shiba chains
• Anomalous Coherence Length of Majorana Zero Modes at Vortices in Superconducting Topological Insulators
• Directly probing the chirality of Majorana edge states
• Majorana Zero Modes in Cylindrical Semiconductor Quantum Wire
• Grain-boundary topological superconductor
• Control of Yu-Shiba-Rusinov States through a Bosonic Mode
• A topological current divider
• Floquet-engineered diode performance in a Majorana-quantum dot Josephson junction
• Topological superconductivity in an ultrathin, magnetically-doped topological insulator proximity coupled to a conventional superconductor
• On the Majorana representation of the optical Dirac equation
• Spin-polarized currents and noise in NS junctions with Yu-Shiba-Rusinov impurities
• Charge-impurity-induced Majorana fermions in topological superconductors
• Anisotropic multiband superconductivity in 2M-WS${}_2$ probed by controlled disorder
• Emergence of Exotic Spin Texture in Supramolecular Metal Complexes on a 2D Superconductor
• Modification of the Optical Properties of Molecular Chains upon Coupling to Adatoms
• Critical Current Anomaly at the Topological Quantum Phase Transition in a Majorana Josephson Junction
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Missing odd-order Shapiro steps do not uniquely indicate fractional Josephson effect
• Optically and electrically controllable adatom spin-orbital dynamics in transition metal dichalcogenides
• Controllable Majorana vortex states in iron-based superconducting nanowires
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Majorana corner pairs in a two-dimensional $s$-wave cold atomic superfluid
• Bound states around impurities in a superconducting bilayer
• Detecting quasi-degenerate ground states in topological models via variational quantum eigensolver
• Universal properties of anyon braiding on one-dimensional wire networks
• Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator
• Impurity-induced subgap states in superconductors with inhomogeneous pairing
• Anisotropic Kondo screening induced by spin-orbit coupling in quantum wires
• Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade
• Majorana Zero Modes in Ferromagnetic Wires without Spin-Orbit Coupling
• In the Pursuit of Majorana Modes in Iron-based High-$T_c$ Superconductors
• Challenges in detecting topological superconducting transitions via supercurrent and phase probes in planar Josephson junctions
• Marginally localized edges of time-reversal symmetric topological superconductors
• Gate-tunable topological superconductivity in a supramolecular electron spin lattice
• High-Resolution Spectroscopy of the Intermediate Impurity States near a Quantum Phase Transition
• Majorana modes in trapped-ion system and their Floquet engineering
• Detrimental effects of disorder in two-dimensional time-reversal invariant topological superconductors
• Predicting topological invariants and unconventional superconducting pairing from density of states and machine learning
• Unified model for non-Abelian braiding of Majorana and Dirac fermion zero modes
• Neel proximity effect in superconductor/antiferromagnet heterostructures
• Probing Magnetic and Triplet Correlations in Spin-Split Superconductors with Magnetic Impurities
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Backscattering off a driven Rashba impurity at the helical edge
• Quantum Hall valley Ferromagnets as a platform for topologically protected quantum memory
• Moiré dispersion of edge states in spin chains on superconductors
• Lifshitz transitions and Weyl semimetals from a topological superconductor with supercurrent flow
• Pairing symmetry in monolayer of orthorhombic CoSb
• Dynamics of a Majorana trijunction in a microwave cavity
• Topological properties of finite-size heterostructures of magnetic topological insulators and superconductors
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• From Ising model to Kitaev Chain -- An introduction to topological phase transitions
• Shaping graphene superconductivity with nanometer precision
• Topological superconductivity in proximity to type-II superconductors
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• RKKY interaction at helical edges of topological superconductors
• Proximity-induced zero-energy states indistinguishable from topological edge states
• Investigation of the Yu-Shiba-Rusinov states of a multi-impurity Kondo system
• Topological phases in the presence of disorder and longer-range couplings
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Asymmetric Transport in Long-Range Interacting Chiral Spin Chains
• Magnetic flux induced higher-order topological superconductivity
• Transport properties of proximitized double quantum dots
• Spin-resolved nonlocal transport in proximitized Rashba nanowires
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Many-body Majorana-like zero modes without gauge symmetry breaking
• Preparation and readout of Majorana qubits in magnet-superconductor hybrid systems
• Tunneling between helical Majorana modes and helical Luttinger liquids
• Theoretical proposal to obtain strong Majorana evidence from scanning tunneling spectroscopy of a vortex with a dissipative environment
• Effects of electron-electron interactions in the Yu-Shiba-Rusinov lattice model
• Photoemission Spectroscopic Evidence of Multiple Dirac Cones in Superconducting BaSn${}_3$
• Mirror-protected Majorana zero modes in $f$-wave multilayer graphene superconductors
• Experimental realization of Majorana hinge and corner modes in intrinsic organic topological superconductor without magnetic field at room temperature
• Superconducting triangular islands as a platform for manipulating Majorana zero modes
• Fractionalization of Majorana-Ising-type quasiparticles
• Superconductivity and vortex structure on Bi${}_2$Te${}_3$/FeTe${}_{0.55}$Se${}_{0.45}$ heterostructures with different thickness of Bi${}_2$Te${}_3$ films
• A proposal for realizing Majorana fermions without external magnetic field in strongly correlated nanowires
• From Majorana fermions to topological quantum computation in semiconductor/superconductor heterostructures
• Subgap modes in two-dimensional magnetic Josephson junctions
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Field-Programmable Topological Array: Framework and Case-Studies
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• Topological Superconductor from the Quantum Hall Phase: Effective Field Theory Description
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Topologically trivial gap-filling in superconducting Fe(Se,Te) by one dimensional defects
• Geometric Manipulation of a Decoherence-Free Subspace in Atomic Ensembles
• Anisotropy of Yu-Shiba-Rusinov states in NbSe${}_2$
• Topological superconductivity driven by correlations and linear defects in multiband superconductors
• Magnetic flux induced topological superconductivity in magnetic atomic rings
• Effects of dynamical noises on Majorana bound states
• Spin Signature of Majorana Fermions in Topological Nodal-Point Superconductors
• Signatures of Amorphous Shiba State in FeTe${}_{0.55}$Se${}_{0.45}$
• Superconductor Vortex Spectrum Including Fermi Arc States in Time-Reversal Symmetric Weyl Semimetals
• Spin and electronic excitations in $4f$ atomic chains on Au(111) substrates
• Anomalous superconducting proximity effect of planar Pb-RhPb2 heterojunctions in the clean limit
• Deterministic topological quantum gates for Majorana qubits without ancillary modes
• Multi-locational Majorana Zero Modes
• The feedback driven atomic scale Josephson microscope
• Andreev bound states at nonmagnetic impurities in superconductor/antiferromagnet heterostructures
• Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder
• Anomalous Shiba spectrum and superconductivity induced magnetic interactions in materials with topological band inversion
• Dynamics of quantum resources in regular and Majorana fermion systems
• Magnetic-field driven evolution of zero-energy mode on Bi islands deposited on Fe(Te,Se)
• Embedded Majorana Islands
• Topological Classification of One-Dimensional Chiral Symmetric Interfaces
• Dynamic-RKKY induced time-reversal symmetry breaking and chiral spin liquids
• Charge-density-wave control by adatom manipulation and its effect on magnetic nanostructures
• Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Thermoelectric fluctuations of interfering Majorana bound states
• Topological Aspects of Antiferromagnets
• Subgap states in superconducting islands
• Universal quantum control over Majorana zero modes
• Moiré-enabled topological superconductivity
• Observation of Yu-Shiba-Rusinov states in superconducting graphene
• Majorana modes in helical altermagnet without net magnetism and spin-orbit coupling
• Phase transitions in quantum dot-Majorana zero mode coupling systems
• Floquet Control of Indirect Exchange Interaction in Periodically Driven Two-Dimensional Electron Systems
• Dissipationless topological quantum computation for Majorana objects in sparse-dense mixed encoding process
• Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge
• Proposal for a scalable charging-energy-protected topological qubit in a quantum spin Hall system
• Effects of Majorana bound states on dissipation and charging in a quantum resistor-capacitor circuit
• Confinement versus interface bound states in spin-orbit coupled nanowires
• Combining quantum spin hall effect and superconductivity in few-layer stanene
• Local spectroscopies across the superconductor-insulator transition
• Band twisting and resilience to disorder in long-range topological superconductors
• Zero-energy Bound States in Nodal Topological Lattice
• Charge dynamics and "in plane" magnetic field I: Rashba-Dresselhauss interaction, Majorana fermions and Aharonov-Casher theorems
• Temperature dependent energy gap for Yu-Shiba-Rusinov states at the quantum phase transition
• Fermi arc criterion for surface Majorana modes in superconducting time-reversal symmetric Weyl semimetals
• Fermi-Level Pinning of Yu-Shiba-Rusinov States in a Superconductor with Weakly Broken Spin-Rotational Invariance
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Memory-Critical Dynamical Buildup of Phonon-Dressed Majorana Fermions
• Ubiquitous missing first Shapiro step in Al-InSb nanosheet Josephson junctions
• Quantum error correction in a time-dependent transverse field Ising model
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Impurity bands in magnetic superconductors with spin density wave
• Odd-parity ground state in dilute Yu-Shiba-Rusinov dimers and chains
• A hierarchy in Majorana non-abelian tests and hidden variable models
• Magnetic Susceptibility of Dirac Fermions, Bi-Sb Alloys, Interacting Bloch Fermions, Dilute Nonmagnetic Alloys, and Kondo Alloys
• Studies of braided non-Abelian anyons using anyonic tensor networks
• A scanning tunneling microscope capable of electron spin resonance and pump-probe spectroscopy at mK temperature and in vector magnetic field
• Direct signatures of $d$-level hybridization and dimerization in magnetic adatom chains on a superconductor
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Confinement-induced Majorana modes in a nodal topological superconductor
• Inversion-symmetric Electron Gases as New Platforms for Topological Planar Josephson Junctions
• Ground state of one-dimensional fermion-phonon systems
• Subgap states and quantum phase transitions in one-dimensional superconductor-ferromagnetic insulator heterostructures
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• Few-body precursors of topological frustration
• Fulde-Ferrell-Larkin-Ovchinnikov state in a superconducting thin film attached to a ferromagnetic cluster
• Nonreciprocal Equilibrium Josephson Effect of Arbitrary Periodicity from Poor Man's Majorana Zero Modes
• Exact solutions for topological surface states of three-dimensional lattice models
• Yu-Shiba-Rusinov multiplets and clusters of multiorbital adatoms in superconducting substrates: Subgap Green's function approach
• Spin-polarized zero-bias peak from a single magnetic impurity at an s-wave superconductor: first-principles study
• Anisotropic superconductivity induced at a hybrid superconducting-semiconducting interface
• Buried Dirac points in quantum spin Hall insulators: Implications for Majorana Kramers pair-based quantum computing
• Majorana edge and end states in planar Josephson junctions
• Ab initio simulation framework for Majorana transport in 2D materials: towards topological quantum computing
• Parity flipping mediated by a quantum dot in Majorana Josephson junctions
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States
• Designer quantum matter in van der Waals heterostructures
• Majorana Bound State leakage to impurity in Su-Schrieffer-Heeger-Rashba scenario
• Majorana bound states in the presence of the half-smeared potential
• A weak topological insulator state in quasi-one-dimensional superconductor TaSe${}_3$
• An Exclusion Principle for Sum-Free Quantum Numbers
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
• Fate of Majorana zero modes by a modified real-space-Pfaffian method and mobility edges in a one-dimensional quasiperiodic lattice
• Gap reopening as a possible signature of coupling between Majorana zero modes in Sn-(Bi,Sb)2(Te,S)3-based Josephson trijunctions
• Field-free Superconducting Diode Effect and Topological Fulde-Ferrell Superconductivity in Altermagnetic Shiba Chains
• Renormalization approach to the superconducting Kondo model
• Dimensional crossover of class D real-space topological invariants
• Spin-dependent tunneling between individual superconducting bound states
• Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
• Zero and Nonzero Energy Majorana Modes in an Extended Kitaev Chain
• Majorana edge modes in isolated wires
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
• Emergent 3D Fermiology and Magnetism in an Intercalated Van der Waals System
• Limits of Thermal Conductance Quantization in Chiral Topological Josephson Junctions
• Evolution of the intertwining correlated topological phases in iron-based superconductor Fe(Te,Se)
• Scanning tunneling microscopy study of helimagnetic monolayer CrBr2 on s-wave superconductor NbSe2: a topologically trivial system due to weak interfacial coupling
• Fluctuation response of a minimal Kitaev chain in nonequilibrium states
• Macroscale three-dimensional proximity effect in disordered normal/superconductor nanocomposites
• Time-reversal symmetric topological superconductivity in Machida-Shibata lattices
• Growth optimization of TaN for superconducting spintronics
• Electron density and compressibility in the Kitaev model with a spatially modulated Phase in the superconducting pairing
• Symmetry-protected topological wire in a topological vacuum
• Extending the planar theory of anyons to quantum wire networks
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Non-Topological Edge-Localized Yu-Shiba-Rusinov States in CrBr${}_3$/NbSe${}_2$ Heterostructures
• Detecting and Distinguishing Majorana Zero Modes with the Scanning Tunneling Microscope
• Density-functional description of materials for topological qubits and superconducting spintronics
• Creating and detecting poor man's Majorana bound states in interacting quantum dots
• Multiplicative Chern insulator
• Gap Anisotropy in Layered Superconductors Due to Rashba and Dresselhaus Spin-Orbit Interactions
• Phase transition and fractionalization in superconducting Kondo lattice model
• Signatures of Topological Transitions in the Spin Susceptibility of Josephson Junctions
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• Biot-Savart law in quantum matter