Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics

Abstract

The existence of edge states and zero energy modes in vortex cores is a hallmark of topologically nontrivial phases realized in various condensed matter systems such as the fractional quantum Hall states, p+ip superconductors, and Z_2 insulators (quantum spin Hall state). We examine this scenario for two dimensional noncentrosymmetric superconductors which allow the parity-mixing of Cooper pairs. It is found that even when the s-wave pairing gap is nonzero, provided that the superconducting gap of spin-triplet pairs is larger than that of spin-singlet pairs, gapless edge states and zero energy Majorana modes in vortex cores emerge, characterizing topological order. Furthermore, it is shown that for Rashba superconductors, the quantum spin Hall effect produced by gapless edge states exists even under an applied magnetic field which breaks time-reversal symmetry provided that the field direction is perpendicular to the propagating direction of the edge modes. This result making a sharp contrast to the Z_2 insulator is due to an accidental symmetry inherent in the Rashba model. It is also demonstrated that in the case with magnetic fields, the non-Abelian statistics of vortices is possible under a particular but realistic condition.

arXiv comment21 pages, 9 figures, a reference and two equations are added, and typos are fixed

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• Interplay between exchange split Dirac and Rashba-type surface states in MnBi${}_2$Te${}_4$/BiTeI interface
• Majorana modes in striped two-dimensional inhomogeneous topological superconductors
• Fully gapped superconductivity without sign reversal in the topological superconductor PbTaSe${}_2$
• Critical Current Anomaly at the Topological Quantum Phase Transition in a Majorana Josephson Junction
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description
• Majorana states in a p-wave superconducting ring
• Hall conductivity in the normal and superconducting phases of the Rashba system with Zeeman field
• RKKY interaction at helical edges of topological superconductors
• Josephson effect in spin-singlet superconductor/ferromagnetic insulator/spin-triplet superconductor junctions with helical $p$-wave states
• Majorana multipole response with magnetic point group symmetry
• Theory of surface spectroscopy for noncentrosymmetric superconductors
• Topological Superfluid in one-dimensional Ultracold Atomic System with Spin-Orbit Coupling
• Theory of metal-insulator transitions in graphite under high magnetic field
• Topological properties of finite-size heterostructures of magnetic topological insulators and superconductors
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Detecting non-Abelian statistics of topological states on a chain of superconducting circuits
• Majorana Zero Modes in Ferromagnetic Wires without Spin-Orbit Coupling
• Non-centrosymmetric superconductors on honeycomb lattice
• The vortex core excitation spectrum in gapped topological d-wave superconductors
• Effect of hybridization symmetry on topological phases of odd-parity multiband superconductors
• Mixed-parity superconductivity near Lifshitz transitions in strongly spin-orbit-coupled metals
• Mixed parity pairing in a dipolar gas
• Manifestation of helical edge states as zero-bias magneto-tunneling-conductance peaks in non-centrosymmetric superconductors
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Experimental realization of Majorana hinge and corner modes in intrinsic organic topological superconductor without magnetic field at room temperature
• Topological phase in a $d_{x^2-y^2}+(p+ip)$ superconductor in presence of spin-density-wave
• Stability of the boundary zero modes in one-dimensional topological superconductors
• Majorana bound states and zero-bias conductance peaks in superconductor/semiconductor nanowire devices
• Momentum space imaging of locally noncentrosymmetric superconductors
• Robustness of Topological Order in Semiconductor-Superconductor Nanowires in the Coulomb Blockade Regime
• Tunneling between helical Majorana modes and helical Luttinger liquids
• Effect of helical edge states on the tunneling conductance in ferromagnet/noncentrosymmetric superconductors junctions
• Duality and topology
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Majorana edge states and topological properties in 1D/2D Rashba semiconductor proximity coupled to iron-based superconductor
• ${}^3$He-R: A Topological $s^{\pm }$ Superfluid with Triplet Pairing
• Orbital angular momentum in a topological superconductor with Chern number higher than $1$
• A New Non-Abelian Topological Phase of Cold Fermi Gases in Anisotropic and Spin-Dependent Optical Lattices
• Phase diagrams of superconducting topological surface states
• Chiral universality class of the normal-superconducting and the exciton condensation transition on the surface of topological insulator
• Tunable zero-energy Dirac and Luttinger nodes in a two-dimensional topological superconductor
• Bulk-boundary correspondence in Josephson Junctions
• Unconventional Pairings and Radial Line Nodes in Inversion Symmetry Broken Superconductors
• Coherence Effects of Caroli-de Gennes-Matricon Modes in Nodal Topological Superconductors
• Manipulation of Majorana states in X-junction geometries
• Euler band topology in superfluids and superconductors
• Generic Weyl phase in the vortex state of quasi-two-dimensional chiral superconductors
• Discovery of the topological surface state in a noncentrosymmetric superconductor BiPd
• Current-induced magnetoresistance hysteresis in the kagome superconductor CsV${}_3$Sb${}_5$
• Weakly Anisotropic Noncentrosymmetric Superconductors with Radial Line Nodes and Thermodynamical Anomalies
• Topological Surface Superconductivity Induced by Hydrostatic Pressure-Enhanced Antisymmetric Spin-Orbit Coupling in Non-Centrosymmetric Superconductor PbTaSe2
• 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
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• Emergence of triplet orbital pairing and non-Abelian states in ultracold multi-orbital optical lattices with quadratic band touching
• Majorana bound states in the presence of the half-smeared potential
• New mechanisms to engineer magnetic skyrmions and topological superconductors
• Rashba spin-orbit coupling and artificially engineered topological superconductors
• Electronic correlations in magnetized helical edge states coupled to s-wave superconductors
• Mixed-pairing superconductivity in 5d Mott insulators with antisymmetric exchange
• Magnetic excitations in the helical Rashba superconductor
• Interplay of Rashba spin-orbit coupling and Coulomb interaction in topological spin-triplet excitonic condensates
• Topological superfluid of spinless Fermi gases in p-band honeycomb optical lattices with on-site rotation
• Adiabatic preparation of a number-conserving atomic Majorana phase
• Majorana Bound State leakage to impurity in Su-Schrieffer-Heeger-Rashba scenario
• Identification of the Majorana edge modes in tight-binding systems based on the Krylov method