Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$

Abstract

Topological superconductors have been theoretically predicted as a new class of time-reversal-invariant superconductors which are fully gapped in the bulk but have protected gapless surface Andreev bound states. In this work, we provide a simple criterion that directly identifies this topological phase in \textit{odd-parity} superconductors. We next propose a two-orbital $U-V$ pairing model for the newly discovered superconductor Cu${}_x$Bi${}_2$Se${}_3$%. Due to its peculiar three-dimensional Dirac band structure, we find that an inter-orbital triplet pairing with odd-parity is favored in a significant part of the phase diagram, and therefore gives rise to a topological superconductor phase. Finally we propose sharp experimental tests of such a pairing symmetry.

4.1 pages, 2 figures

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• Weyl Phases in Point-Group Symmetric Superconductors
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• Dominant $s$-wave superconducting gap in PdTe${}_2$ observed by tunneling spectroscopy on side-junctions
• Spin-singlet superconductivity in doped topological crystalline insulator Sn_{0.96}In_{0.04}Te
• Prediction of Nontrivial Band Topology and Superconductivity in Mg${}_2$Pb
• Nematic superconductivity in Cu${}_x$Bi${}_2$Se${}_3$: The surface Andreev bound states
• Fractionalized topological insulators from frustrated spin models in three dimensions
• Topological insulator ribbon: Surface states and dynamical response
• Surface states and local spin susceptibility in doped three-dimensional topological insulators with odd-parity superconducting pairing symmetry
• General theory of robustness against disorder in multi-band superconductors
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• Nematic superconductivity in the topological semimetal CaSn${}_3$
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Twofold symmetry of proximity-induced superconductivity in Bi${}_2$Te${}_3$/Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ heterostructures revealed by scanning tunneling microscopy
• Majorana multipole response: General theory and application to wallpaper groups
• Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor
• $Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions
• Friedel oscillations and Majorana zero modes in inhomogeneous superconductors
• Topological Superconductivity without Proximity Effect
• Fermi-arc metals
• Proximity induced time-reversal topological superconductivity in Bi2Se3 films without phase tuning
• Chemical Principles of Intrinsic Topological Superconductors
• Critical Temperature Enhancement of Topological Superconductors: A Dynamical Mean Field Study
• Topological superconductor in quasi-one-dimensional Tl2-xMo6Se6
• Topological Larkin-Ovchinnikov phase and Majorana zero mode chain in bilayer superconducting topological insulator films
• Dirty two-band superconductivity with interband pairing order
• Time-reversal symmetry breaking in superconductors through loop super-current order
• Internal pressure in superconducting Cu intercalated Bi${}_2$Se${}_3$
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Type I superconductivity in Dirac materials
• Antichiral and nematicity-wave superconductivity
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Thermoelectric detection of Andreev states in unconventional superconductors
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• Violation of Emergent Rotational Symmetry in the Hexagonal Kagome Superconductor CsV3Sb5
• Emergent chiral symmetry in a three-dimensional interacting Dirac liquid
• Strong-Coupling Superconductivity with $T_c$ $\sim$ 10.8 K Induced by P Doping in the Topological Semimetal Mo${}_5$Si${}_3$
• Single branch of chiral Majorana modes from doubly degenerate Fermi surfaces
• Symmetry of superconducting pairing in non-pseudospin electron bands
• Quantum transport in topological insulator hybrid structures -- A combination of topological insulator and superconductor
• Topological superconductivity mediated by magnons of helical magnetic states
• Tailoring phase transition from topological superconductor to trivial superconductor induced by magnetic textures of a spin-chain on a $p$-wave superconductor
• Nematicity of correlated systems driven by anisotropic chemical phase separation
• The effect of interorbital scattering on superconductivity in doped Dirac materials
• Crystal structure and distortion of superconducting Cu${}_x$Bi${}_2$Se${}_3$
• Field-angle-dependent low-energy excitations around a vortex in the superconducting topological insulator CuxBi2Se3
• Type-I and type-II topological nodal superconductors with $s$-wave interaction
• Observation of the topological Dirac fermions and surface states in superconducting BaSn3
• Multiple odd-parity superconducting phases in bilayer transition metal dichalcogenides
• Green function theory of dirty two-band superconductivity
• Nematic superconductivity in topological insulators induced by hexagonal warping
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Symmetry-protected topological invariant and Majorana impurity states in time-reversal-invariant superconductors
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Impurity effects in a two-dimensional topological superconductor: A link of Tc-robustness with a topological number
• Can bilayer graphene become a fractional metal?
• Effective low energy theory for surface Andreev bound states of superconducting phases in generalized Bernevig-Hughes-Zhang models
• Fermiology of possible topological superconductor Tl0.5Bi2Te3 derived from hole-doped topological insulator
• Unitary Symmetry-Protected Non-Abelian Statistics of Majorana Modes
• Disorder effects on thermal transport on the surface of topological superconductors by the self-consistent Born approximation
• Conduction spectroscopy of a proximity induced superconducting topological insulator
• Zero-Energy Modes on Superconducting Bismuth Islands Deposited on Fe(Te,Se)
• Time-Reversal Invariant Topological Superconductivity in Planar Josephson Bijunction
• The Vertical Position of Sr Dopants in the Sr${}_x$Bi${}_2$Se${}_3$ Superconductor
• Superconductivity and Quantum Oscillations in Single Crystals of the Compensated Semimetal CaSb${}_2$
• Quasi-2D Fermi surface of superconducting line-nodal metal CaSb${}_2$
• Magnetic response of nematic superconductors: skyrmion stripes and their signatures in muon spin relaxation experiments
• Symmetries, Length Scales, Magnetic Response and Skyrmion Chains in Nematic Superconductors
• Enhancing triplet superconductivity by the proximity to a singlet superconductor in oxide heterostructures
• Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials
• Superconductivity by alloying the topological insulator SnBi2Te4
• Dual topological superconducting states in the layered titanium-based oxypnictide superconductor BaTi${}_2$Sb${}_2$O
• $R$RuB${}_2$ ($R$=Y, Lu), topological superconductor candidates with hourglass-type Dirac ring
• Strong magnetic field induces superconductivity in Weyl semi - metal
• Two elementary band representation model, Fermi surface nesting, and surface topological superconductivity in $A$V${}_3$Sb${}_5$ ($A=\text{K, Rb, Cs}$)
• Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry
• Odd-Parity Spin-Triplet Superconductivity in Centrosymmetric Antiferromagnetic Metals
• From local spin nematicity to altermagnets: Footprints of band topology
• Weyl point immersed in a continuous spectrum: an example from superconducting nanostructures
• Spin-Nernst Effect in Time-Reversal-Invariant Topological Superconductors
• Topological superconductivity on the honeycomb lattice: Effect of normal state topology
• Dirac fermion and superconductivity in two-dimensional transition-metal MOH (M= Zr, Hf )
• Spontaneous strain and magnetization in doped topological insulators with nematic and chiral superconductivity
• Pairing mechanism of unconventional superconductivity in doped Kane-Mele model
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Observation of spin-polarized surface states in a nodal line semimetal SnTaS${}_2$
• Chiral Gravitomagnetic Effect in Topological Superconductors and Superfluids
• Electric Multipoles of Double Majorana Kramers Pairs
• Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields
• Quantum anomalous Hall effect with field-tunable Chern number near Z2 topological critical point
• Superconductivity in Cu-doped Bi${}_2$Se${}_3$ with potential disorder
• Pair-breaking in superconductors with strong spin-orbit coupling
• Berezinskii-Kosterlitz-Thouless transition transport in spin-triplet superconductor
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• Nodal gap detection through polar angle-resolved density of states measurements in uniaxial superconductors
• Edge superconducting state in attractive U Kane-Mele-Hubbard model
• Effect of impurities on the Josephson current through helical metals: Exploiting a neutrino paradigm
• Visualizing the $d$-vector in a nematic triplet superconductor
• Observability of superconductivity in Sr-doped Bi2Se3 at the surface using scanning tunneling microscope
• Tunable Coupling of Two-Dimensional Superconductors in Bilayer SrTiO3 Heterostructures
• Lifshitz transition in dirty nematic superconductor
• Effects on the Non-Relativistic Dynamics of a Charged Particle Interacting with a Chern-Simons Potential
• Nodeless superconducting gap in the candidate topological superconductor Sn${}_{1-x}$In${}_x$Te for x = 0.7
• Superconducting properties of Cu intercalated Bi${}_2$Se${}_3$ studied by Muon Spin Spectroscopy
• Converting topological insulators into topological metals within the tetradymite family
• Quasiparticle interference in doped topological insulators with nematic superconductivity
• An increase in $T_c$ under hydrostatic pressure in the superconducting doped topological insulator Nb${}_{0.25}$Bi${}_2$Se${}_3$
• Control of Edge Currents at a Ferromagnet - Triplet Superconductor Interface by Multiple Helical Majorana Modes
• Accessing topological superconductivity via a combined STM and renormalization group analysis
• Magnetic tilting and emergent Majorana spin connection in topological superconductors
• Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing
• Triplet superconductivity in 3D Dirac semimetal due to exchange interaction
• Topological s-wave pairing superconductivity with spatial inhomogeneity: Mid-gap-state appearance and robustness of superconductivity
• Chiral topological superconducting state with Chern number $\mathcal{C}=-2$ in Pb${}_3$Bi/Ge(111)
• Induced topological order at the boundary of 3D topological superconductors
• Anomalous Coherence Length of Majorana Zero Modes at Vortices in Superconducting Topological Insulators
• Full superconducting gap in the candidate topological superconductor In${}_{1-x}$Pb${}_x$Te for x = 0.2
• Nuclear magnetic relaxation rates of unconventional superconductivity in doped topological insulators
• Proximity effect of time-reversal symmetry broken non-centrosymmetric superconductors
• Anomalous Shiba states in topological iron-based superconductors
• Bardasis-Schrieffer-like phase mode in a superconducting bilayer
• Anisotropic Upper Critical Field, Seebeck and Nernst Coefficient in Nb0.20Bi2Se3 Topological Superconductor
• Andreev spectroscopy of Majorana states in topological superconductors with multipocket Fermi surfaces
• Pressure Engineering of the Dirac Fermions in Quasi-One-Dimensional Tl${}_2$Mo${}_6$Se${}_6$
• Superconductivity and weak anti-localization in nodal-line semimetal SnTaS_2
• Chiral to helical Majorana fermion transition in a $p$-wave superconductor
• Interface currents and magnetization in singlet-triplet superconducting heterostructures: Role of chiral and helical domains
• Controllable enhancement of $p$-wave superconductivity via magnetic coupling to a conventional superconductor
• Fully gapped superconductivity without sign reversal in the topological superconductor PbTaSe${}_2$
• Topology of superconductors beyond mean-field theory
• Manipulating the nematic director by magnetic fields in the spin-triplet superconducting state of CuxBi2Se3
• Probing the topological character of superconductors via non-local Hanbury-Brown and Twiss correlations
• Multi-band Eilenberger theory of superconductivity: Systematic low-energy projection
• Emergence of Topological Superconductivity in Doped Topological Dirac Semimetals under Symmetry-Lowering Lattice Distortions
• Topological superconductivity in an ultrathin, magnetically-doped topological insulator proximity coupled to a conventional superconductor
• Inverse coherence effects in nuclear magnetic relaxation rates as a sign of topological superconductivity
• Magnification of signatures of topological phase transition by quantum zero point motion
• Pauli paramagnetism of triplet Cooper pairs in a nematic superconductor
• Electron dynamics in topological insulator based semiconductor-metal interfaces (topological p-n interface based on Bi2Se3 class)
• Three-dimensional symmetry breaking topological matters
• Bound states around impurities in a superconducting bilayer
• Elementary models of 3D topological insulators with chiral symmetry
• Anisotropic multiband superconductivity in 2M-WS${}_2$ probed by controlled disorder
• Low-energy phonons and superconductivity in Sn${}_{0.8}$In${}_{0.2}$Te
• Superconductive proximity in a Topological Insulator slab and excitations bound to an axial vortex
• Strongly suppressed superconducting proximity effect and ferromagnetism in trilayers of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ / $\mathrm{SrRu}{\mathrm{O}}_3$ / underdoped $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{\mathrm{x}}$: A possible new platform for Majorana nano-electronics
• Introduction of Sr into Bi2Se3 thin films by molecular beam epitaxy
• Visualizing Pairing Symmetry in Nematic Superconductors using spin-polarized spectroscopy of magnetic impurities
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Detrimental effects of disorder in two-dimensional time-reversal invariant topological superconductors
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Strain induced spin vortex and Majorana Kramer's pairs in doped topological insulators with nematic superconductivity
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Nematic order driven by superconducting correlations
• Effect of hybridization symmetry on topological phases of odd-parity multiband superconductors
• Surface Spectral Function of Momentum-dependent Pairing Potentials in a Topological Insulator: Application to Cu${}_x$Bi${}_2$Se${}_3$
• Quantized thermal and spin transports of dirty planar topological superconductors
• Three-dimensional time reversal invariant topological superconductivity in doped chiral topological semimetals
• $\mu$SR and magnetometry study of superconducting 5% Pt doped IrTe${}_2$
• Hybrid symmetry class topological insulators
• Topology-insensitive axion mass in magnetic topological insulators
• Incommensuration in odd-parity antiferromagnets
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Helical Topological Superconducting Pairing at Finite Excitation Energies
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Upper magnetic field in superconducting Dirac semi-metal
• Signatures of surface Majorana modes in the magnetic response of topological superconductors
• Photoemission Spectroscopic Evidence of Multiple Dirac Cones in Superconducting BaSn${}_3$
• Representation-protected topology of spin-singlet $s$-wave superconductors
• Odd-parity topological superfluidity for fermions in a bond-centered square optical lattice
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Majorana edge states and topological properties in 1D/2D Rashba semiconductor proximity coupled to iron-based superconductor
• Rotating Majorana Zero Modes in a disk geometry
• Spontaneous Lattice Distortion in the Spin-Triplet Superconductor Cu${}_x$Bi${}_2$Se${}_3$
• Superconducting and normal-state anisotropy of the doped topological insulator Sr${}_{0.1}$Bi${}_2$Se${}_3$
• Temperature tuned Fermi surface topology and segmentation in non-centrosymmetric superconductors
• Theory of tunneling spectroscopy in a superconducting topological insulator
• Phase diagrams of superconducting topological surface states
• Possible two-component pairings in electron-doped Bi${}_2$Se${}_3$ based on a tight-binding model
• The feedback driven atomic scale Josephson microscope
• Anomalous Shiba spectrum and superconductivity induced magnetic interactions in materials with topological band inversion
• Quantized bound states around a vortex in anisotropic superconductors
• Chiral universality class of the normal-superconducting and the exciton condensation transition on the surface of topological insulator
• Superconductivity in doped planar Dirac insulators: A renormalization group study
• First-order chiral to non-chiral transition in the angular dependence of the upper critical induction of the Scharnberg-Klemm $p$-wave pair state
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Engineering Helical Superconductors with Multiple Majorana Kramers Pairs via Higher-Order Rashba Spin-Orbit Coupling
• Resolving phonon-mediated superconducting pairing symmetries from first-principles calculation
• Majorana Flat Bands in the Vortex Line of Superconducting Weyl Semimetals
• Interaction between spin and Abrikosov vortices in doped topological insulators
• Anomalous Josephson Hall effect in doped topological insulators with the nematic superconductivity
• Particle-hole spectral asymmetry at the edge of multiorbital noncentrosymmetric superconductors
• Generic Weyl phase in the vortex state of quasi-two-dimensional chiral superconductors
• Surface chiral superconductivity in odd-parity nematic superconductors with magnetic impurities
• Solving two-dimensional non-relativistic electronic and muonic atoms governed by Chern-Simon potential
• On the existence of nematic-superconducting states in the Ginzburg-Landau regime
• Tunneling and bound states in near-edge NbN-$\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ junctions fabricated by deposition through a wire shadow mask
• Effects of iron doping on the topological insulator surfaces
• 3D Non-Abelian Anyons: Degeneracy Splitting and Detection by Adiabatic Cooling
• Revisiting vestigial order in nematic superconductors: gauge-field mechanisms and model constraints
• Electronic structures and stability investigation of the new class of large band gap topological insulators MTl${}_4$Te${}_3$ (M = Cd, Hg)
• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• Intrinsic chiral topological superconductor thin films
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Surface states around a vortex in topological superconductors: Intersection of a surface and a vortex
• Unconventional superconductivity from electronic dipole fluctuations
• Topological Surface Superconductivity Induced by Hydrostatic Pressure-Enhanced Antisymmetric Spin-Orbit Coupling in Non-Centrosymmetric Superconductor PbTaSe2
• Superconductivity in three-dimensional interacting doped topological insulators
• Unconventional superconducting correlations in fermionic many-body scars
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Simple model for the gap in the surface states of the antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Pressure induced superconductivity bordering a charge-density-wave state in NbTe4 with strong spinorbit coupling
• Theory of low-energy behaviors in topological $s$-wave pairing superconductors
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• A theorem regarding families of topologically non-trivial fermionic systems
• Strain-induced Berry phase in chiral superconductors
• Binary kagome superconducting candidates hosting topological electronic states
• Magnetic impurities make superconductivity in 3D Dirac semi-metal triplet
• Single-gap Isotropic $s-$wave Superconductivity in Single Crystals ${\text{AuSn}}_4$
• Simple Models for All Topological Phases
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal