From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires

Abstract

Electronic excitations above the ground state must overcome an energy gap in superconductors with spatially-homogeneous s-wave pairing. In contrast, inhomogeneous superconductors such as those with magnetic impurities or weak links, or heterojunctions containing normal metals or quantum dots, can host subgap electronic excitations that are generically known as Andreev bound states (ABSs). With the advent of topological superconductivity, a new kind of ABS with exotic qualities, known as Majorana bound state (MBS), has been discovered. We review the main properties of ABSs and MBSs, and the state-of-the-art techniques for their detection. We focus on hybrid superconductor-semiconductor nanowires, possibly coupled to quantum dots, as one of the most flexible and promising experimental platforms. We discuss how the combined effect of spin-orbit coupling and Zeeman field in these wires triggers the transition from ABSs into MBSs. We show theoretical progress beyond minimal models in understanding experiments, including the possibility of different types of robust zero modes that may emerge without a band-topological transition. We examine the role of spatial non-locality, a special property of MBS wavefunctions that, together with non-Abelian braiding, is the key to realizing topological quantum computation.

Review. 23 pages, 8 figures, 1 table. Shareable published version by Springer Nature at https://rdcu.be/b7DWT (free to read but not to download)

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• Local and non-local quantum transport due to Andreev bound states in finite Rashba nanowires with superconducting and normal sections
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• Enhancing the Josephson diode effect with Majorana bound states
• Plateau regions for zero-bias peaks within 5% of the quantized conductance value $2e^2/h$
• Closing of the Induced Gap in a Hybrid Superconductor-Semiconductor Nanowire
• Majorana bound states in semiconducting nanostructures
• Distinguishing trivial and topological zero energy states in long nanowire junctions
• Parity protected superconducting diode effect in topological Josephson junctions
• Trivial Andreev band mimicking topological bulk gap reopening in the non-local conductance of long Rashba nanowires
• Probing Majorana localization in minimal Kitaev chains through a quantum dot
• Large zero bias peaks and dips in a four-terminal thin InAs-Al nanowire device
• Selective area epitaxy of PbTe-Pb hybrid nanowires on a lattice-matched substrate
• Josephson effect and odd-frequency pairing in superconducting junctions with unconventional magnets
• Two-Impurity Yu-Shiba-Rusinov States in Coupled Quantum Dots
• Spin-resolved thermal signatures of Majorana-Kondo interplay in double quantum dots
• Majorana-like Coulomb spectroscopy in the absence of zero bias peaks
• Exceptional odd-frequency pairing in non-Hermitian superconducting systems
• Helical Liquids in Semiconductors
• Signatures of Majorana protection in a three-site Kitaev chain
• Non-Majorana modes in diluted spin chains proximitized to a superconductor
• Numerical study of PbTe-Pb hybrid nanowires for engineering Majorana zero modes
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• Linear and non-linear transport across a finite Kitaev chain: an exact analytical study
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• Enhanced topological superconductivity in spatially modulated planar Josephson junctions
• Large even-odd spacing and $g$-factor anisotropy in PbTe quantum dots
• Majorana Bound States Induced by Antiferromagnetic Skyrmion Textures
• Evidence for spin-polarized bound states in semiconductor-superconductor-ferromagnetic insulator islands
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• Adversarial Hamiltonian learning of quantum dots in a minimal Kitaev chain
• Observation of edge and bulk states in a three-site Kitaev chain
• Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires
• Recent progress on Majorana in semiconductor-superconductor heterostructures--Engineering and detection
• Fibonacci anyons versus Majorana fermions
• Anomalous Floquet Chiral Topological Superconductivity in a Topological Insulator Sandwich Structure
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Scanning tunneling spectroscopy of Majorana zero modes in a Kitaev spin liquid
• Supercurrent reversal in ferromagnetic hybrid nanowire Josephson junctions
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene
• Dynamical polarization of the fermion parity in a nanowire Josephson junction
• Tunable proximity effects and topological superconductivity in ferromagnetic hybrid nanowires
• Crossed Andreev reflection in spin-polarized chiral edge states due to the Meissner effect
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• Pinning of Andreev bound states to zero energy in two-dimensional superconductor-semiconductor Rashba heterostructures
• Conductance Quantization in PbTe Nanowires
• Non-Hermitian phase-biased Josephson junctions
• Full parity phase diagram of a proximitized nanowire island
• Identifying Majorana bound states by tunneling shot-noise tomography
• Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions
• Single-shot fabrication of semiconducting-superconducting nanowire devices
• Semiconductor-ferromagnet-superconductor planar heterostructures for 1D topological superconductivity
• Quadrupole spin polarization as signature of second-order topological superconductors
• Majorana mode leaking into a spin-charge entangled double quantum dot
• Coupled superconducting spin qubits with spin-orbit interaction
• Ballistic PbTe Nanowire Devices
• Observation of Aharonov-Bohm effect in PbTe nanowire networks
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• Evidence of Andreev blockade in a double quantum dot coupled to a superconductor
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• Hybridization mechanism of the dual proximity effect in superconductor-topological insulator interfaces
• Cooper pairs localization in tree-like networks of superconducting islands
• InP/GaSb core-shell nanowires: a novel hole-based platform with strong spin-orbit coupling for full-shell hybrid devices
• Majorana-magnon interactions in topological Shiba chains
• Simulation of Kitaev model using one-dimensional chain of superconducting qubits and environmental effect on topological states
• Universal conductance dips and fractional excitations in a two-subband quantum wire
• Signatures of Kondo-Majorana interplay in ac response
• Magnon-mediated topological superconductivity in a quantum wire
• Transient effects in quantum dots contacted via topological superconductor
• Implementation of single-qubit gates via parametric modulation in the Majorana transmon
• Charging a Dimerized Quantum XY Chain
• Probing Majorana bound states via a pn-junction containing a quantum dot
• Stabilizing topological superconductivity in disordered spin-orbit coupled semiconductor-superconductor heterostructures
• Current and shot noise in a normal metal-superconductor junction driven by spin-dependent periodic pulse sequence
• Quasiparticle poisoning in trivial and topological Josephson junctions
• The topological Kondo model out of equilibrium
• Anomalous proximity effect under Andreev and Majorana bound states
• Topological gap protocol based machine learning optimization of Majorana hybrid wires
• Photonic cross-noise spectroscopy of Majorana bound states
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Nonlocal correlations transmitted between quantum dots via short topological superconductor
• Topological Josephson Bifurcation Amplifier: Semiclassical theory
• Reply to "Comment on 'Trivial Andreev Band Mimicking Topological Bulk Gap Reopening in the Nonlocal Conductance of Long Rashba Nanowires'"
• Enhanced $2\pi$-periodic Aharonov-Bohm Effect as a Signature of Majorana Zero Modes Probed by Nonlocal Measurements
• Richardson model with complex level structure and spin-orbit coupling for hybrid superconducting islands: stepwise suppression of pairing and magnetic pinning
• Spatially Dependent in-Gap States Induced by Andreev Tunneling through a Single Electronic State
• Gate-tunable topological superconductivity in a supramolecular electron spin lattice
• Fate of the superconducting state in floating islands of hybrid nanowire devices
• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Quantum transport theory of hybrid superconducting systems
• Atomistic modeling of a superconductor-transition-metal dichalcogenide-superconductor Josephson junction
• Tomasch Oscillations as Above-Gap Signature of Topological Superconductivity
• Coexistence of topological and nontopological Fermi-superfluid phases
• Dressed Majorana fermion in a hybrid nanowire
• Strongly correlated electrons in superconducting islands with fluctuating Cooper pairs
• Quantized Andreev conductance in semiconductor nanowires
• Spin Signature of Majorana Fermions in Topological Nodal-Point Superconductors
• Mirror-protected Majorana zero modes in $f$-wave multilayer graphene superconductors
• A proposal for realizing Majorana fermions without external magnetic field in strongly correlated nanowires
• Conductance asymmetry in proximitized magnetic topological insulator junctions with Majorana modes
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Honing in on a topological zero-bias conductance peak
• Spin-resolved nonlocal transport in proximitized Rashba nanowires
• Noise-Tolerance of Majorana Teleportation in Mesoscopic Topological Superconductors
• Relations between normal state nonreciprocal transport and the superconducting diode effect in the trivial and topological phases
• The differential conductance tunnel spectroscopy in an analytical solvable two-terminal Majorana device
• Transport of Majorana Bound State in the presence of telegraph noise
• Caroli-de Gennes-Matricon Analogs in Full-Shell Hybrid Nanowires
• Phase-controlled minimal Kitaev chain in multiterminal Josephson junctions
• Theory of superconducting proximity effect in hole-based hybrid semiconductor-superconductor devices
• Anisotropy of PbTe nanowires with and without a superconductor
• Fluxoid valve effect in full-shell nanowire Josephson junctions
• Engineering subgap states in superconductors by the symmetry of altermagnetism
• Electron transport in quantum channels with spin-orbit interaction: Effects of the sign of the Rashba coupling and applications to nanowires
• Quantum dot coupled to topological insulators: The role of edge states
• In situ tuning of dynamical Coulomb blockade on Andreev bound states in hybrid nanowire devices
• Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena
• Vertex correction for the linear and nonlinear optical responses in superconductors: multiband effect and topological superconductivity
• Re-entrant topological order in strongly correlated nanowire due to Rashba spin-orbit coupling
• Embedded Majorana Islands
• Super-Poissonian noise from quasiparticle poisoning in electron transport through a pair of Majorana bound states
• Phase transitions in quantum dot-Majorana zero mode coupling systems
• Topological zero modes and bounded modes at smooth domain walls: Exact solutions and dualities
• Non-Abelian holonomy of Majorana zero modes coupled to a chaotic quantum dot
• Gate-tunable negative differential conductance in hybrid semiconductor-superconductor devices
• Majorana modes in helical altermagnet without net magnetism and spin-orbit coupling
• Transport-based fusion that distinguishes between Majorana and Andreev bound states
• Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations in the quasi-ballistic regime in phase-pure GaAs/InAs core/shell nanowires
• Repulsive Casimir force from a Majorana zero-mode
• Majorana polarization in disordered heterostructures
• Non-Abelian anyon statistics through AC conductance of a Majorana interferometer
• Strong enhancement of g-factor in PbTe-Pb hybrid nanowires
• Exponential suppression of the topological gap in self-consistent intrinsic Majorana nanowires
• Ab initio study of Proximity-Induced Superconductivity in PbTe/Pb heterostructures
• Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions
• Tight-Binding Energy-Phase Calculation for Topological Josephson Junction Nanowire Architecture
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• Antichiral edge states and Bogoliubov Fermi surfaces in a two-dimensional proximity-induced superconductor
• Solitonic Andreev spin qubits from Andreev states in Corbino Josephson junctions
• Supercurrent modulation in InSb nanoflag-based Josephson junctions by scanning gate microscopy
• The Josephson effect in Fibonacci superconductors
• Subgap states and quantum phase transitions in one-dimensional superconductor-ferromagnetic insulator heterostructures
• Persistent current noise in narrow Josephson junctions
• Enhanced Thermoelectricity in Nanowires with inhomogeneous Helical states
• AI-enhanced tuning of quantum dot Hamiltonians toward Majorana modes
• Robust quantized thermal conductance of Majorana floating edge bands in d-wave superconductors
• Confinement-induced zero-bias peaks in conventional superconductor hybrids
• Quantum-size effect induced Andreev bound states in ultrathin metallic islands proximitized by a superconductor
• Andreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling
• Particle-hole spectral asymmetry at the edge of multiorbital noncentrosymmetric superconductors
• Confinement-induced Majorana modes in a nodal topological superconductor
• Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems
• Qubit based on spin-singlet Yu-Shiba-Rusinov states
• Andreev molecule in parallel InAs nanowires
• Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
• Electron-hole coherence in core-shell nanowires with partial proximity induced superconductivity
• Quantifying proximity-induced superconductivity from first-principles calculations
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
• Giant and robust Josephson diode effect in multiband topological nanowires
• Fluxoid solitons in superconducting tapered tubes and bottlenecks
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes
• Spin responses of a disordered helical superconducting edge under Zeeman field
• Majorana modes in graphene strips: polarization, wavefunctions, disorder, and Andreev states
• Determination of the current-phase relation of an InAs 2DEG Josephson junction with a microwave resonator
• Coulomb blockade in open superconducting islands on InAs nanowires
• Presence versus absence of charging energies in PbTe quantum dots
• Parity readout in Majorana box qubits from the dispersive to the resonant regime
• Absence of Quasi-Majorana False Positives in Full-Shell Hybrid Nanowires
• Non-Topological Edge-Localized Yu-Shiba-Rusinov States in CrBr${}_3$/NbSe${}_2$ Heterostructures
• Creating and detecting poor man's Majorana bound states in interacting quantum dots
• Cross-correlation mediated by Majorana island with finite charging energy
• SWAP gate between a Majorana qubit and a parity-protected superconducting qubit
• Drastic effect of weak interaction near special points in semiclassical multiterminal superconducting nanostructures
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method
• Tunable effective length of fractional Josephson junctions
• Transient triplet blockade in Andreev junction
• Realizing Majorana Kramers pairs in two-channel InAs-Al nanowires with highly misaligned electric fields
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States
• Proximity-induced superconductivity generated by thin films: Effects of Fermi surface mismatch and disorder in the superconductor
• Majorana bound states with chiral magnetic textures
• Green Function Invariants for Floquet Topological Superconductivity Induced by Proximity Effects
• Electronic transport in double-nanowire superconducting islands with multiple terminals
• Entanglement dynamics in minimal Kitaev chains
• Enhanced Andreev Reflection in Flat-Band Systems: Wave Packet Dynamics, DC Transport and the Josephson Effect
• Magnetically tuned topological phase in graphene nanoribbon heterojunctions
• Unveiling In-Gap States and Majorana Zero Modes in Superconductor-Topological Insulator Bilayer model
• Gate-controlled Supercurrent in Ballistic InSb Nanoflag Josephson Junctions