Majorana Zero Modes and Topological Quantum Computation

Abstract

We provide a current perspective on the rapidly developing field of Majorana zero modes in solid state systems. We emphasize the theoretical prediction, experimental realization, and potential use of Majorana zero modes in future information processing devices through braiding-based topological quantum computation. Well-separated Majorana zero modes should manifest non-Abelian braiding statistics suitable for unitary gate operations for topological quantum computation. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localized at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic Majorana zero modes in solid state systems. We also discuss fractional quantum Hall systems (the 5/2 state) in this context. We describe proposed schemes for carrying out braiding with Majorana zero modes as well as the necessary steps for implementing topological quantum computation.

Final Version Accepted for Publication as a Review Article in NPJ Quantum Information

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• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Topological superconductivity in Landau levels
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Differential current noise as an identifier of Andreev bound states that induce nearly quantized conductance plateaus
• Emergent strong zero mode through local Floquet engineering
• Renormalization of the Majorana bound state decay length in a perpendicular magnetic field
• Proposal for measuring the parity anomaly in a topological superconductor ring
• Role of the quasi-particles in an electric circuit with Josephson junctions
• Electrostatical formation of the Majorana quasiparticles in the quantum dot--nanoring structure
• Majorana phase-gate based on the geometric phase
• Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• 1D Majorana Goldstinos and partial supersymmetry breaking in quantum wires
• Phase space methods for Majorana fermions
• Topological contextuality and anyonic statistics of photonic-encoded parafermions
• Exciting odd frequency equal-spin-triplet correlations at metal-superconductor interfaces
• Majorana orthogonal transformation and Majorana zero modes in free fermionic systems
• Universal topological quantum computation with strongly correlated Majorana edge modes
• Disordered Majorana nanowires: Studying disorder without any disorder
• Atomic diffusion-induced polarization and superconductivity in topological insulator-based heterostructures
• Non-Hermitian minimal Kitaev chains
• Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates
• Dispersive sensing in hybrid InAs/Al nanowires
• Magnetically-textured superconductivity in elemental Rhenium
• Stability of Disordered Topological Superconducting Phases in Magnet--Superconductor Hybrid Systems
• Universal quantum computing with parafermions assisted by a half fluxon
• Properties of the Majorana-state tunneling Josephson junction mediated by an interacting quantum dot
• Curvature of gap closing features and the extraction of Majorana nanowire parameters
• Randomized measurement protocols for lattice gauge theories
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing
• Transport properties of Majorana bound states networks in the Coulomb blockade regime
• First Principles Assessment of CdTe as a Tunnel Barrier at the $\alpha$-Sn/InSb Interface
• Majorana signatures in charge transport through a topological superconducting double-island system
• Coulomb Blockade in Fractional Topological Superconductors
• Continuous error correction for Ising anyons
• Observation of the topological Dirac fermions and surface states in superconducting BaSn3
• Chiral twodimensional p-wave superfluid from s-wave pairing in the BEC regime
• Erasing odd-parity states in semiconductor quantum dots coupled to superconductors
• Emergent pair symmetries in systems with poor man's Majorana modes
• Eight-vertex criticality in the interacting Kitaev chain
• Machine Learning the Disorder Landscape of Majorana Nanowires
• Effect of topological length on Bound states signatures in a Topological nanowire
• Fault-tolerant hyperbolic Floquet quantum error correcting codes
• Engineering Quantum Hall Phases in Synthetic Bilayer Graphene System
• Multi-level effects in quantum-dot based parity-to-charge conversion of Majorana box qubits
• Quantum transport in coupled Majorana box systems
• Gapless odd-frequency superconductivity induced by the Sachdev-Ye-Kitaev model
• Probing edge state conductance in ultra-thin topological insulator films
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Conditions allowing error correction in driven qubits
• Dual topological superconducting states in the layered titanium-based oxypnictide superconductor BaTi${}_2$Sb${}_2$O
• Electron-Tunneling-Assisted Non-Abelian Braiding of Rotating Majorana Bound States
• Strain manipulation of Majorana fermions in graphene armchair nanoribbons
• Engineering Quantum Spin Liquids and Many-Body Majorana States with a Driven Superconducting Box Circuit
• Tunable interface states between Floquet-Weyl semimetals
• Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid
• Chiral current-phase relation of topological Josephson junctions: A signature of the $4\pi$-periodic Josephson effect
• Low-temperature environments for quantum computation and quantum simulation
• Increased localization of Majorana modes in antiferromagnetic chains on superconductors
• Statistical Majorana Bound State Spectroscopy
• Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields
• Absence of Majorana oscillations in finite-length full-shell hybrid nanowires
• Majorana stripe order on the surface of a three-dimensional topological insulator
• Topological superconductor candidates PdBi${}_2$Te${}_4$ and PdBi${}_2$Te${}_5$ from a generic ab initio strategy
• Majorana-mediated thermoelectric transport in multiterminal junctions
• Do Rydberg chains yield Fibonacci anyons?
• Visualization by scanning SQUID microscopy of the intermediate state in the superconducting Dirac semimetal PdTe${}_2$
• Observation of in-gap states in a two-dimensional CrI2/NbSe2 heterostructure
• Quench dynamics of entanglement spectrum and topological superconducting phases in a long-range Hamiltonian
• Phase-Controllable Nonlocal Spin Polarization in Proximitized Nanowires
• Tunable topological states hosted by unconventional superconductors with adatoms
• Accurate projective two-band description of topological superfluidity in spin-orbit-coupled Fermi gases
• Higher-order topological superconductivity in monolayer WTe${}_2$ from repulsive interactions
• Versatile Large-Area Custom-Feature van der Waals Epitaxy of Topological Insulators
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Full counting statistics in a Majorana single-charge transistor
• Bosonization of Majorana modes and edge states
• Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer
• Optimizing the topological properties of stacking semiconductor-ferromagnet-superconductor heterostructures
• Complete description of fault-tolerant quantum gate operations for topological Majorana qubit systems
• Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors
• Topological superconductivity in a magnetic-texture coupled Josephson junction
• Electronic structure of InAs and InSb surfaces: density functional theory and angle-resolved photoemission spectroscopy
• Degradability of Fermionic Gaussian Channels
• Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach
• Geometric presentations of braid groups for particles on a graph
• Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases
• Topological antiferromagnetic spintronics: Part of a collection of reviews on antiferromagnetic spintronics
• Quantum Criticality in Resonant Andreev Conduction
• Signature of pressure-induced topological phase transition in ZrTe${}_5$
• Majorana excitons in a Kitaev chain of semiconductor quantum dots in a nanowire
• Switchable Non-Hermitian Skin Effect in Bogoliubov Modes
• Ground state topology of a four-terminal superconducting double quantum dot
• Scaling up a sign-ordered Kitaev chain without magnetic flux control
• Revisiting 2-pi phase slip suppression in topological Josephson junctions
• An optical investigation of the heavy fermion normal state in superconducting UTe${}_2$
• Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors
• Proximity-Induced Superconductivity in Atomically Precise Nanographene
• Quantum dots as parafermion detectors
• Electrostatic effects and topological superconductivity in semiconductor-superconductor-magnetic insulator hybrid wires
• Nonlinearity and Topology
• Stabilization of a Majorana Zero Mode through Quantum Frustration
• Non-thermal eigenstates and slow relaxation in quantum Fredkin spin chains
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Read-Green points and level crossings in XXZ central spin models and $p_x+i{p}_y$ topological superconductors
• Dirac Fermions and Topological Phases in Magnetic Topological Insulator Films
• Odd-frequency pairing in a superconductor coupled to two parallel nanowires
• Phase jumps in Josephson junctions with time-dependent spin-orbit coupling
• Microwave Signatures of Topological Superconductivity in Planar Josephson Junctions
• Frustration-free Hamiltonians supporting Majorana zero edge modes
• Dynamical approach to improving Majorana qubits and distinguishing them from trivial bound states
• Detailed magneto-heat capacity analysis of SnAs topological superconductor
• Nonequilibrium Andreev bound states population in short superconducting junctions coupled to a resonator
• Two types of dark solitons in a spin-orbit-coupled Fermi gas
• High critical temperature nodal superconductors as building block for time-reversal invariant topological superconductivity
• Transport probe of nonadiabatic transition caused by Majorana moving
• Vision transformer based Deep Learning of Topological indicators in Majorana Nanowires
• Topological Protection of Coherence in Noisy Open Quantum Systems
• Directly probing the chirality of Majorana edge states
• Optical signatures of Euler superconductors
• Josephson current via an isolated Majorana zero mode
• Strong spin-dephasing in a topological insulator - paramagnet heterostructure
• Error-correction properties of an interacting topological insulator
• Effects of spin-orbit coupling and in-plane Zeeman fields on the critical current in two-dimensional hole gas SNS junctions
• InP/GaSb core-shell nanowires: a novel hole-based platform with strong spin-orbit coupling for full-shell hybrid devices
• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Almost Strong Zero Modes at Finite Temperature
• Simulation of Kitaev model using one-dimensional chain of superconducting qubits and environmental effect on topological states
• Nodal superconducting gap structure and topological surface states of UTe${}_2$
• Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions
• Phonon-induced Majorana Qubit Relaxation in Tunnel-Coupled Two-Island Topological Superconductors
• Probing details of spin--orbit coupling through Pauli spin blockade
• Long range $p$-wave proximity effect into a disordered metal
• Topological Quantum Computation on a Chiral Kondo Chain
• Hilbert space structure of the low energy sector of U(N) quantum Hall ferromagnets and their classical limit
• Anomalous proximity effect under Andreev and Majorana bound states
• Fractional transconductance via non-adiabatic topological Cooper pair pumping
• Anisotropic multiband superconductivity in 2M-WS${}_2$ probed by controlled disorder
• Chiral topological superconductivity in Josephson junction
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• Strong and Weak Three-Dimensional Topological Insulators Probed by Surface Science Methods
• Edge ${\mathbb{Z}}_3$ parafermions in fermionic lattices
• Critical properties of the Majorana chain with competing interactions
• Quantum spin Hall states in the lateral heteromonolayers of WTe2-MoTe2
• Origin of robust exceptional points: a restricted bulk zero mode
• Observation of an Abrupt 3D-2D Morphological Transition in Thin Al Layers Grown by MBE on InGaAs surface
• Topological gap protocol based machine learning optimization of Majorana hybrid wires
• Dynamical torques from Shiba states in $s$-wave superconductors
• Coexistence of Chiral Majorana Edge States and Bogoliubov Fermi Surfaces in Two-Dimensional Nonsymmorphic Dirac Semimetal/Superconductor Heterostructures
• Majorana modes in striped two-dimensional inhomogeneous topological superconductors
• Majorana Zero Modes in Nanowires with Combined Triangular and Hexagonal Geometry
• Topological reflection matrix
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Dynamical signatures of ground-state degeneracy to discriminate against Andreev levels in a Majorana fusion experiment
• Braids and phase gates through high-frequency virtual tunneling of Majorana Zero Modes
• All-electrical spectroscopy of topological phases in semiconductor-superconductor heterostructures
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Dynamics of a Majorana trijunction in a microwave cavity
• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Implementing Majorana fermions in a cold-atom honeycomb lattice with textured pairings
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Optimal Conditions for Observing Fractional Josephson Effect in Topological Josephson Junctions
• Full counting statistics of the currents through a Kitaev chain and the exchange fluctuation theorem
• Gapless state of interacting Majorana fermions in a strain-induced Landau level
• Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides
• Coexistence of topological and nontopological Fermi-superfluid phases
• Mixed-parity superconductivity near Lifshitz transitions in strongly spin-orbit-coupled metals
• Prediction of topological superconductivity in 1$T$-TiTe${}_2$ under pressure
• Second-order topological insulator in periodically driven lattice
• Atomic scale imaging of sign-changing order parameter in superconducting FeSe with Tunneling Andreev Reflection
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites
• In the Pursuit of Majorana Modes in Iron-based High-$T_c$ Superconductors
• Boson-fermion pairing and condensation in two-dimensional Bose-Fermi mixtures
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• Probing the non-Abelian fusion of a pair of Majorana zero modes
• Band bending profile and band offset extraction at semiconductor-metal interfaces
• Symmetry Aspects of Chiral Superconductors
• Sub-symmetry Protected Topology in Topological Insulators and Superconductors
• Maximal distant entanglement in Kitaev tube
• Majorana corner states in square and Kagome quantum spin liquids
• Three-dimensional time reversal invariant topological superconductivity in doped chiral topological semimetals
• Majorana Zero Modes in Fermionic Wires coupled by Aharonov-Bohm Cages
• Edge state behavior in a Su-Schrieffer-Heeger like model with periodically modulated hopping
• Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade
• Type-II topological phase transitions of topological skyrmion phases
• Universal Signatures of Majorana-like Quasiparticles in Strongly Correlated Landau-Fermi Liquids
• Dynamic crystallization in a quantum Ising chain
• Probing Magnetic and Triplet Correlations in Spin-Split Superconductors with Magnetic Impurities
• Physics of the Majorana-superconducting qubit hybrids
• Disorder Suppression in Topological Semiconductor-Superconductor Junctions
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Interface engineering of van der Waals heterostructures towards energy-efficient quantum devices operating at high temperatures
• Polynomial description of inhomogeneous topological superconducting wires
• Exotic quantum statistics and thermodynamics from a number-conserving theory of Majorana fermions
• Altermagnet-Superconductor Heterostructure: a Scalable Platform for Braiding of Majorana Modes
• Complete zero-energy flat bands of surface states in fully gapped chiral noncentrosymmetric superconductors
• Fractionalization of Majorana-Ising-type quasiparticles
• Engineering subgap states in superconductors by the symmetry of altermagnetism
• Ising quantum criticality in Majorana nanowires
• Noise-Tolerance of Majorana Teleportation in Mesoscopic Topological Superconductors
• Synthetic anyons in noninteracting systems
• Creation and manipulation of surface code defects with quantum optimal control
• Refined Phase Diagram for a Spin-1 System Exhibiting a Haldane Phase
• Probing the dichotomy between Yu-Shiba-Rusinov and Majorana bound states via conductance, quantum noise and ${\Delta }_T$ noise
• Theoretical proposal to obtain strong Majorana evidence from scanning tunneling spectroscopy of a vortex with a dissipative environment
• Erasure conversion in Majorana qubits via local quasiparticle detection
• Majorana bound states and zero-bias conductance peaks in superconductor/semiconductor nanowire devices
• Synthetic spin-orbit coupling mediated by a bosonic environment
• Pumped heat and charge statistics from Majorana braiding
• Circulator function in a Josephson junction circuit and braiding of Majorana zero modes
• Kinetic stabilization of 1D surface states near twin boundaries in noncentrosymmetric BiPd
• Transport of Majorana Bound State in the presence of telegraph noise
• Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model
• Self-consistent quasi-particle $GW$ and hybrid functional calculations for Al/InAs/Al heterojunctions: band offset and spin-orbit coupling effects
• Zero-bias conductance peaks at zero applied magnetic field due to stray fields from integrated micromagnets in hybrid nanowire quantum dots
• Topological Computation by non-Abelian Braiding in Classical Metamaterials
• Topological Superconductor from the Quantum Hall Phase: Effective Field Theory Description
• Fragmentation, Zero Modes, and Collective Bound States in Constrained Models
• Current-phase relation of a short multi-mode Bi2Se3 topological insulator nanoribbon Josephson junction with ballistic transport modes
• A proposal for realizing Majorana fermions without external magnetic field in strongly correlated nanowires
• Superconducting topological Dirac semimetals: $P6/m$-Si${}_6$ and $P6/m$-NaSi${}_6$
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations
• Coherent transfer of topological domain walls
• Influence of disorder on antidot vortex Majorana states in 3D topological insulators
• Anomalous Shiba spectrum and superconductivity induced magnetic interactions in materials with topological band inversion
• Development of research network on Quantum Annealing Computation and Information using Google Scholar data
• Quantized bound states around a vortex in anisotropic superconductors
• Topological zero modes and bounded modes at smooth domain walls: Exact solutions and dualities
• Chiral superfluid helium-3 in the quasi-two-dimensional limit
• Observation of Yu-Shiba-Rusinov states in superconducting graphene
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
• Multi-locational Majorana Zero Modes
• Re-entrant topological order in strongly correlated nanowire due to Rashba spin-orbit coupling
• Deterministic topological quantum gates for Majorana qubits without ancillary modes
• Hexagonal warping effect to Majorana zero modes at ends of superconducting vortex line in doped 3D strong topological insulators
• Symmetry defects and their application to topological quantum computing
• A unified numerical approach to semiconductor-superconductor heterostructures
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Diagonal Entropy and Topological Phase Transitions in Extended Kitaev Chains
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Enhancement in surface mobility and quantum transport of Bi_(2-x)Sb_(x)Te_(3-y)Se_(y) topological insulator by controlling the crystal growth conditions
• Characterizing local Majorana properties using Andreev states
• Majorana bound state parity exchanges in planar Josephson junctions
• Topological Aspects of Antiferromagnets
• Universal quantum control over Majorana zero modes
• Majorana braiding simulations with projective measurements
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Direct observation of the surface superconducting gap in the topological superconductor candidate β-PdBi2
• Spin-helical detection in a semiconductor quantum device with ferromagnetic contacts
• Majorana modes in helical altermagnet without net magnetism and spin-orbit coupling
• Dissipationless topological quantum computation for Majorana objects in sparse-dense mixed encoding process
• Topological Josephson junction in transverse magnetic field
• Non-Abelian operation through scattering between chiral Dirac edge modes
• Helical and topological phase detection based on nonlocal conductance measurements in a three terminal junction
• Protected ground states in short chains of coupled spins in circuit quantum electrodynamics
• Fidelity of the Kitaev honeycomb model under a quench
• Surface induced odd-frequency spin-triplet superconductivity as a veritable signature of Majorana bound states
• Robust quantisation of circular photogalvanic effect in multiplicative topological semimetals
• Repulsive Casimir force from a Majorana zero-mode
• Double-dot interferometer for quantum measurement of Majorana qubits and stabilizers
• Transport and fusion of Majorana zero modes in the presence of nonadiabatic transitions
• Electrical, thermal and thermoelectric transport in open long-range Kitaev chain
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• A Computer Code for Topological Quantum Spin Systems over Triangulated Surfaces
• Surface chiral superconductivity in odd-parity nematic superconductors with magnetic impurities
• Cross correlation mediated by distant Majorana zero modes with no overlap
• Observable-enriched entanglement
• Manipulation of Majorana wave packets at surfaces of nodal noncentrosymmetric superconductors
• Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems
• The ZX-calculus as a Language for Topological Quantum Computation
• In-plane magnetic field driven conductance modulations in topological insulator kinks
• Dynamical simulation of the injection of vortices into a Majorana edge mode
• Spin dependent conductance of a quantum dot side attached to topological superconductors as a probe of Majorana fermion states
• Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization
• Laughlin charge pumping from interplay of chiral Dirac and chiral Majorana modes
• Quantum dot detects Majorana modes of both chiralities
• Suppressing decoherence in quantum state transfer with unitary operations
• Andreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling
• Intrinsic chiral topological superconductor thin films
• Confinement-induced zero-bias peaks in conventional superconductor hybrids
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model
• Chromium chalcohalide Janus monolayer ferromagnets with perpendicular magnetic anisotropy and high Curie temperature
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Strong and almost strong modes of Floquet spin chains in Krylov subspaces
• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Andreev Reflections in NbN/graphene Junctions under Large Magnetic Fields
• Non-Abelian interference of topological edge states
• Pressure-induced Superconductivity in Noncentrosymmetric Weyl Semimetals LaAlX (X = Si and Ge)
• Majorana edge states in s-wave kagome superconductors with Rashba interaction
• Topological in-gap chiral edge states in superconducting Haldane model with spin-orbit coupling
• Mitigating disorder and optimizing topological indicators with vision-transformer-based neural networks in Majorana nanowires
• Quantized conductance in a one-dimensional ballistic oxide nanodevice
• Topotactic Growth of Zintl Phase Eu${}_5$In${}_2$As${}_6$ Nanowires with Antiferromagnetic Behavior
• Sub-gap Fano resonances in a topological superconducting wire with on-site Coulomb interactions
• Solitonic Andreev spin qubits from Andreev states in Corbino Josephson junctions
• Magnus effect on a Majorana zero-mode
• DC-current induced domain wall in a chiral $p$-wave superconductor
• Fermion zero modes in a $Z_2$ vortex background
• Multiterminal Josephson junctions with tunable topological properties
• Non-Hermitian Effects in the Su-Schrieffer-Heeger model: Exploring Substrate Coupling and Decoupling Dynamics
• Cross-correlation mediated by Majorana island with finite charging energy
• Index theory and noncommutative geometry of topological insulator
• Adiabatic preparation of a number-conserving atomic Majorana phase
• Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes
• Color codes with domino twists: Construction, logical measurements, and computation
• Josephson and persistent currents in a quantum ring between topological superconductors
• Robust interface-state laser in non-Hermitian micro-resonator arrays
• The possible coexistence of superconductivity and topological electronic states in 1T-RhSeTe
• Solving Sharp Bounded-error Quantum Polynomial Time Problem by Evolution methods
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Determination of the current-phase relation of an InAs 2DEG Josephson junction with a microwave resonator
• Impact of static disorder on quasiparticle spectra: Debye-Waller, mean free path and potential fluctuation effects
• Majorana Conductances in Three-Terminal Transports
• Majorana qubit readout by a point-contact detector under finite bias voltages
• Electron-hole Hybridization in Bilayer Graphene
• SWAP gate between a Majorana qubit and a parity-protected superconducting qubit
• Scheme for braiding Majorana zero modes in vortices using an STT-matrix
• Massless Majorana bispinors and two-qubit entangled state
• 'Stealth' singularities from self-gravitating fermions
• Introduction to Majorana Zero Modes in a Kitaev Chain
• Decoherence of Majorana zero modes mediated by gapless fermions
• Ballistic transport in 1D Rashba systems in the context of Majorana nanowires
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• Spin responses of a disordered helical superconducting edge under Zeeman field
• Many-body wave function and edge magnetization of an open $p+is$ superconducting chain
• Superconducting Proximity Effect in an SSH-Superconductor Junction
• Entanglement dynamics in minimal Kitaev chains
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
• Quantum capacitance and parity switching of a quantum-dot-based Kitaev chain
• Topologically nontrivial multicritical points
• Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures
• Kagome edge states under lattice termination, spin-orbit coupling, and magnetic order
• Excess photon-assisted noise of Majorana and Andreev bound states
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward
• Optimal Majoranas in Mesoscopic Kitaev Chains
• Ultracold atomic lattice systems for simulating topological phases: A review
• Superfluidity of identical fermions in an optical lattice: atoms and polar molecules
• Observation of the crossover from quantum fluxoid to half-quantum fluxoid in a chiral superconducting device
• Rashba spin-orbit coupling and artificially engineered topological superconductors
• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization
• Quasiparticle Interference of Spin-Triplet Superconductors: Application to UTe${}_2$
• Long-range Cooper pair splitting by chiral Majorana edge states
• Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra
• Time-reversal symmetric topological superconductivity in Machida-Shibata lattices
• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed $s$- and $d$-wave symmetries
• Transport through Nodal Surface Semimetal-Superconductor junction in absence/presence of light irradiation
• Temperature-Dependent Collective Excitations in a Three-Dimensional Dirac System ZrTe${}_5$
• Edge dependence of the Josephson current in the quantum Hall regime
• Embedding 1D BDI topological dynamics into continuous elastic plates
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method
• Anomalous spin textures in a 2D topological superconductor induced by point impurities
• Light Control of Triplet Pairing in Correlated Electrons with Mixed-Sign Interactions
• 2D Gapless Topological Superfluids Generated by Pairing Phases
• Unveiling topological order through multipartite entanglement
• Proximity-induced superconductivity generated by thin films: Effects of Fermi surface mismatch and disorder in the superconductor
• Tunable effective length of fractional Josephson junctions
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Emergent One-Dimensional Helical Channel in Higher-Order Topological Insulators with Step Edges
• Majorana bound states with chiral magnetic textures
• Majorana flat bands at structured surfaces of nodal noncentrosymmetric superconductors
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Majorana-like oscillation for edge states in one-dimensional topological chain with dissipative couplings
• Spin-polarized zero-bias peak from a single magnetic impurity at an s-wave superconductor: first-principles study
• An exactly solvable model for anyons with non-Abelian flux