Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors

Abstract

The non-Abelian topological order for superconductors is characterized by the existence of zero-energy Majorana fermions in edges of systems and in a vortex of a macroscopic condensate, which obey the non-Abelian statistics. This paper is devoted to an extensive study on the non-Abelian topological phase of spin-singlet superconductors with the Rashba spin-orbit interaction proposed in our previous letter [M. Sato, Y. Takahashi, and S. Fujimoto, Phys. Rev. Lett. 103, 020401 (2009)]. We mainly consider the s-wave pairing state and the d+id pairing state. In the case of d+id-wave pairing, Majorana fermions appear in almost all parameter regions of the mixed state under an applied magnetic field, provided that the Fermi level crosses k-points in the vicinity of the Gamma point or the M point in the Brillouin zone, while in the case of s-wave pairing, a strong magnetic field, the Zeeman energy of which is larger than the superconducting gap is required to realize the topological phase. We clarify that Majorana fermions in Rashba spin-singlet superconductors are much more stable than those realized in spin-triplet p+ip superconductors in certain parameter regions. We also investigate the topological number which ensures the topological stability of the phase in detail. Furthermore, as a byproduct, we found that topological order is also realized in conventional spin (or charge) density wave states with the Rashba spin-orbit interaction, for which massless Dirac fermions appear in the edge of the systems and charge fractionalization occurs.

arXiv comment38 pages, 10 figures. two figures, references and appendix c are added

References in corpus (45)

• Fault-tolerant quantum computation by anyons
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Majorana fermions in a tunable semiconductor device
• Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Experimental Study of the BEC-BCS Crossover Region in Lithium 6
• Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Superconductivty without inversion symmetry: MnSi versus CePt_3Si
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Electrically detected interferometry of Majorana fermions in a topological insulator
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice
• Superfluid analogies of cosmological phenomena
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• Topological odd-parity superconductors
• Spin Hall effects for cold atoms in a light induced gauge potential
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• Electron Correlation and Pairing States in Superconductors without Inversion Symmetry
• Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
• Geometric phases and quantum entanglement as building blocks for nonabelian quasiparticle statistics
• Superconductivity in CoO${}_2$ Layers and the Resonating Valence Bond Mean Field Theory of the Triangular Lattice t-J model
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Line nodes in the superconducting gap function of noncentrosymmetric CePt_3Si
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Doped t-J Model on a Triangular Lattice: Possible Application to Na${}_x$CoO${}_2\cdot y$H${}_2$0 and Na${}_{1-x}$TiO${}_2$
• Fusion rules and vortices in $p_x+i{p}_y$ superconductors
• Non-equilibrium spin dynamics in a trapped Fermi gas with effective spin-orbit interaction
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Topological Order and Non-Abelian Statistics in Noncentrosymmetric s-Wave Superconductors
• Enhancement of Superconducting Transition Temperature due to the strong Antiferromagnetic Spin Fluctuations in Non-centrosymmetric Heavy-fermion Superconductor CeIrSi3 :A 29Si-NMR Study under Pressure
• Non-Abelian Statistics of Axion Strings
• Fermi liquid theory for heavy fermion superconductors without inversion symmetry : Magnetism and transport coefficients
• Colossal enhancement of upper critical fields in noncentrosymmetric heavy fermion superconductors near quantum criticality: CeRhSi${}_3$ and CeIrSi${}_3$
• Majorana bound state in rotating superfluid 3He-A between parallel plates

Cited by in corpus (207)

• Topological insulators and superconductors
• Search for Majorana fermions in superconductors
• Topological superconductors: a review
• Symmetry and Topology in Non-Hermitian Physics
• Introduction to topological superconductivity and Majorana fermions
• Chiral superconductivity from repulsive interactions in doped graphene
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Topology of crystalline insulators and superconductors
• Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states
• Majorana Fermions and Topology in Superconductors
• Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
• Probing Atomic Structure and Majorana Wavefunctions in Mono-Atomic Fe-chains on Superconducting Pb-Surface
• Topology of Andreev Bound States with Flat Dispersion
• Majorana qubit decoherence by quasiparticle poisoning
• Random-matrix theory of Majorana fermions and topological superconductors
• Competing many-body instabilities and unconventional superconductivity in graphene
• Nature of unconventional pairing in the kagome superconductors AV${}_3$Sb${}_5$
• Probing anisotropic superfluidity of rashbons in atomic Fermi gases
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Chiral d-wave superconductivity in doped graphene
• Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
• Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to Sr2RuO4
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• Majorana Fermions in Nodal Superconductors: Gapless Topological Phase
• Tunneling Conductance and Surface States Transition in Superconducting Topological Insulators
• Majorana nanowires for topological quantum computation
• Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions : Approach From Bulk Calculations
• Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
• On controlling the bound states in quantum-dot hybrid-nanowire
• Majorana edge states in two atomic wires coupled by pair-hopping
• Topological Superconductivity and Majorana Fermions in Metallic Surface-States
• Edge properties of the chiral d-wave superconducting state in doped graphene
• Pairing with dominant triplet component and possible weak topological superconductivity in BiS${}_2$-based superconductors
• Majorana Fermion Induced Non-local Current Correlations in Spin-orbit Coupled Superconducting Wires
• Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures
• Rashba spin-orbit coupled atomic Fermi gases
• Visualising Majorana bound states in 1D and 2D using the generalized Majorana polarization
• Local and non-local quantum transport due to Andreev bound states in finite Rashba nanowires with superconducting and normal sections
• A comprehensive review on topological superconducting materials and interfaces
• Majorana Fermions and Multiple Topological Phase Transition in Kitaev Ladder Topological Superconductors
• Topologically non-trivial superconductivity in spin-orbit coupled systems: Bulk phases and quantum phase transitions
• Majorana Braiding Dynamics on Nanowires
• Majorana bound states in open quasi-1D and 2D systems with transverse Rashba coupling
• Inhomogeneous Topological Superfluidity in One-Dimensional Spin-Orbit-Coupled Fermi Gases
• Majorana bound states in semiconducting nanostructures
• Topological Crystalline Superconductivity in Locally Non-centrosymmetric Multilayer Superconductors
• Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
• Bulk electronic state of superconducting topological insulator
• STM as a single Majorana detector of Kitaev's chiral spin liquid
• Nodeless superconductivity in noncentrosymmetric PbTaSe${}_2$ single crystals
• Trivial Andreev band mimicking topological bulk gap reopening in the non-local conductance of long Rashba nanowires
• Majorana fermions in pinned vortices
• Spin-polarized edge currents and Majorana fermions in one- and two-dimensional topological superconductors
• Spin-orbit-coupled ferroelectric superconductivity
• Spin-Triplet Vortex State in the Topological Superconductor CuxBi2Se3
• Local density of states in metal - topological superconductor hybrid systems
• Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability
• Spontaneous currents in a superconductor with s+is symmetry
• Topological superconductivity in quasicrystals
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Time reversal invariant topological superconductivity in correlated non-centrosymmetric systems
• Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field
• Tunneling spectrum of a pinned vortex with a robust Majorana state
• Odd-frequency pair in topological superconductivity of 1D magnetic chain
• Superconducting doped topological materials
• Multiorbital Ferroelectric Superconductivity in doped SrTiO3
• Majorana flat bands, chiral Majorana edge states, and unidirectional Majorana edge states in noncentrosymmetric superconductors
• Reentrant topological transitions in a quantum wire/superconductor system with quasiperiodic lattice modulation
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Zero-energy bound states in the high-temperature superconductors at the two-dimensional limit
• Majorana fermions in spin-orbit coupled ferromagnetic Josephson junctions
• Paramagnetically induced gapful topological superconductors
• Chiral Majorana Modes via Proximity to a Twisted Cuprate Bilayer
• Vortex states and Majorana fermions in spin-orbit coupled semiconductor-superconductor hybrid structures
• Majorana states in inhomogeneous spin ladders
• Topological superfluids on a lattice with non-Abelian gauge fields
• Majorana fermions on a disordered triangular lattice
• Odd-frequency pairing and proximity effect in Kitaev chain systems including topological critical point
• Entangling Spins in Double Quantum Dots and Majorana Bound States
• Majorana bound state localization and energy oscillations for magnetic impurity chains on conventional superconductors
• Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization
• Majorana fermions in s-wave noncentrosymmetric superconductor with Rashba and Dresselhaus (110) spin-orbit couplings
• Microscopic theory for a ferromagnetic-nanowire/superconductor heterostructure: Transport, fluctuations and topological superconductivity
• Pinning of Andreev bound states to zero energy in two-dimensional superconductor-semiconductor Rashba heterostructures
• Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-
• Heterostructural one-unit-cell FeSe/SrTiO3: from high-temperature superconductivity to topological states
• Non-magnetic impurity effects in a three-dimensional topological superconductor: From p- to s-wave behaviors
• Impurity bound states in fully gapped $d$-wave superconductors with subdominant order parameters
• Identification of topological superconductivity in magnetic impurity systems using bulk spin-polarization
• Quasi-classical theory of tunneling spectroscopy in superconducting topological insulator
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• 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
• Phonon anomaly and anisotropic superconducting gap in non-centrosymmetric Li2(Pd1-xPtx)3B
• Entanglement Spectrum as a Probe for the Topology of a Spin-Orbit Coupled Superconductor
• Non-Abelian toplogical superconductors from topological semimetals and related systems under superconducting proximity effect
• Geometric Josephson effects in chiral topological nanowires
• Majorana fermions at odd junctions in a wire network of ferromagnetic impurities
• Superconducting monolayer deposited on substrate: effects of the spin-orbit coupling induced by proximity effects
• Majorana fermion from Landau quantization in 2D topological superconductors
• Topological D+p-wave superconductivity in Rashba systems
• Majorana bound states in a superconducting Rashba nanowire in the presence of antiferromagnetic order
• Quench Dynamics of Josephson Current in a Topological Josephson Junction
• Probing vortex Majorana fermions and topology in semiconductor-superconductor heterostructures
• Manifestation of chirality in the vortex lattice in a two-dimensional topological superconductor
• Theory of tunneling spectroscopy for chiral topological superconductors
• Magnetoelectric coupling in superconductor-helimagnet heterostructures
• Odd-frequency Cooper pair amplitude around a vortex core in a chiral p-wave superconductor in the quantum limit
• Simulating Z_2 topological insulators via a one-dimensional cavity optomechanical cells array
• Unusual Zeeman-field effects in two-dimensional spin-orbit-coupled Fermi superfluids
• Probing Majorana-like states in quantum dots and quantum rings
• Dimerization-induced topological superconductivity in a Rashba nanowire
• Probing chiral edge states in topological superconductors through spin-polarized local density of state measurements
• Quantum geometry encoded to pair potentials
• Momentum-Space Spin Texture in a Topological Superconductor
• Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor
• Consequences of integrability breaking in quench dynamics of pairing Hamiltonians
• Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor
• Superconducting Sn_{1-x}In_{x}Te Nanoplates
• Topological Superconductivity without Proximity Effect
• Majorana bound states in magnetic impurity chains: effects of $d$-wave pairing
• Topological superconductivity in Fibonacci quasicrystals
• Topological superconductivity at finite temperatures in proximitized magnetic nanowires
• Critical Temperature Enhancement of Topological Superconductors: A Dynamical Mean Field Study
• Fully gapped superconductivity with preserved time reversal symmetry in noncentrosymmetric LaPdIn
• Edge currents as a probe of the strongly spin-polarized topological noncentrosymmetric superconductors
• Josephson diode effect with Andreev and Majorana bound states
• Electrostatical formation of the Majorana quasiparticles in the quantum dot--nanoring structure
• Theory of tunneling conductance of anomalous Rashba metal / superconductor junctions
• Non-equilibrium topological phase transitions in two-dimensional optical lattices
• Supercurrent-Induced Spin-Orbit Torques
• Interplay between singlet and triplet pairings in multi-band two-dimensional oxide superconductors
• Stability of Disordered Topological Superconducting Phases in Magnet--Superconductor Hybrid Systems
• Phase segregation of superconductivity and ferromagnetism at LaAlO${}_3$/SrTiO${}_3$ interface
• Skyrmion spin texture in ferromagnetic semiconductor-superconductor heterostructures
• Integrability of an extended d+id-wave pairing Hamiltonian
• Impurity effects in a two-dimensional topological superconductor: A link of Tc-robustness with a topological number
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Chiral twodimensional p-wave superfluid from s-wave pairing in the BEC regime
• Nodeless superconductivity in noncentrosymmetric LaRhSn
• First principles study of topological phase in chains of $3d$ transition metals
• Flux-induced Topological Superconductor in Planar Josephson Junction
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
• Non-Hermiticity stabilized Majorana zero modes in semiconductor-superconductor nanowires
• Majorana end states in an interacting quantum wire
• Delocalisation of Majorana quasiparticles in plaquette--nanowire hybrid system
• Topological spin-singlet superconductors with underlying sublattice structure
• Quantum engineering of Majorana quasiparticles in one-dimensional optical lattices
• Tunable vortex bound states in multiband CsV3Sb5-derived kagome superconductors
• Topological superconductivity on the honeycomb lattice: Effect of normal state topology
• Probing the chirality of 1D Majorana edge states around a 2D nanoflake in a superconductor
• Interaction proximity effect at the interface between a superconductor and a topological insulator quantum well
• Accurate projective two-band description of topological superfluidity in spin-orbit-coupled Fermi gases
• Chiral f-wave Topological Superuid in Triangular Optical Lattices
• Non-adiabatic dynamics of superfluid spin-orbit coupled degenerate Fermi gas
• Accessing topological superconductivity via a combined STM and renormalization group analysis
• Zeeman field induced non-trivial topology in a spin-orbit coupled superconductor
• Leakage of the Majorana quasiparticles in Rashba nanowire deposited on superconducting--normal substrate
• Topological Phases in Nodeless Tetragonal Superconductors
• Majorana-Weyl cones in ferroelectric superconductors
• Majorana Zero Modes in Semiconductor Nanowires in Contact with Higher-$T_c$ Superconductors
• Self-consistent study of topological superconductivity in two-dimensional quasicrystals
• Engineering topological superconductors using surface atomic-layer/molecule hybrid materials
• Nonlinear optical responses in superconductors under magnetic fields: quantum geometry and topological superconductivity
• Topological s-wave pairing superconductivity with spatial inhomogeneity: Mid-gap-state appearance and robustness of superconductivity
• Topological quantum phase transitions in the spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings
• Enhanced $2\pi$-periodic Aharonov-Bohm Effect as a Signature of Majorana Zero Modes Probed by Nonlocal Measurements
• Superconducting pairing symmetry in MoTe${}_2$
• Non-adiabatic dynamics in d+id-wave fermionic superfluids
• Multi-band Eilenberger theory of superconductivity: Systematic low-energy projection
• Pairing instabilities in topological insulator quantum wells
• Effects of anisotropic correlations in fermionic zero-energy bound states of topological phases
• Coexistence of topological and nontopological Fermi-superfluid phases
• Two-dimensional Paired Topological Superfluids of Rydberg Fermi Gases
• Spin singlet topological superconductivity in the attractive Rashba Hubbard model
• Majorana bound states in d-wave superconductor planar Josephson junction
• Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals
• Majorana transport in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings
• Topological Phase Separation In Trapped Ultracold Fermionic Gases
• Topological phase transitions in superconductors with chiral symmetry
• Majorana bound states and zero-bias conductance peaks in superconductor/semiconductor nanowire devices
• A New Non-Abelian Topological Phase of Cold Fermi Gases in Anisotropic and Spin-Dependent Optical Lattices
• Vertex correction for the linear and nonlinear optical responses in superconductors: multiband effect and topological superconductivity
• Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires
• Topological phases in twisted Rashba superconductors
• Gapless superconductivity and its real-space topology in quasicrystals
• Quantum Degenerate Majorana Surface Zero Modes in Two-Dimensional Space
• Optical-vortex-pulse induced nonequilibrium spin textures in spin-orbit coupled electrons
• Andreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling
• Generic Weyl phase in the vortex state of quasi-two-dimensional chiral superconductors
• Triplet character of 2D-fermion dimers arising from $s$-wave attraction via spin-orbit coupling and Zeeman splitting
• Majorana Bound State leakage to impurity in Su-Schrieffer-Heeger-Rashba scenario
• Floquet first- and higher-order topological superconductors: A review
• Majorana bound states in the presence of the half-smeared potential
• Majorana bound states with chiral magnetic textures
• Chiral topological superconductivity in twisted bilayer and double bilayer graphene
• Observation of the crossover from quantum fluxoid to half-quantum fluxoid in a chiral superconducting device
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method
• Electronic correlations in magnetized helical edge states coupled to s-wave superconductors
• Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes
• Emergence of triplet orbital pairing and non-Abelian states in ultracold multi-orbital optical lattices with quadratic band touching
• Entanglement dynamics in minimal Kitaev chains
• Topological superfluid of spinless Fermi gases in p-band honeycomb optical lattices with on-site rotation