Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -

Abstract

Superconductivity is a phenomenon where the macroscopic quantum coherence appears due to the pairing of electrons. This offers a fascinating arena to study the physics of broken gauge symmetry. However, the important symmetries in superconductors are not only the gauge invariance. Especially, the symmetry properties of the pairing, i.e., the parity and spin-singlet/spin-triplet, determine the physical properties of the superconducting state. Recently it has been recognized that there is the important third symmetry of the pair amplitude, i.e., even or odd parity with respect to the frequency. The conventional uniform superconducting states correspond to the even-frequency pairing, but the recent finding is that the odd-frequency pair amplitude arises in the spatially non-uniform situation quite ubiquitously. Especially, this is the case in the Andreev bound state (ABS) appearing at the surface/interface of the sample. The other important recent development is on the nontrivial topological aspects of superconductors. As the band insulators are classified by topological indices into (i) conventional insulator, (ii) quantum Hall insulator, and (iii) topological insulator, also are the gapped superconductors. The influence of the nontrivial topology of the bulk states appears as the edge or surface of the sample. In the superconductors, this leads to the formation of zero energy ABS (ZEABS). Therefore, the ABSs of the superconductors are the place where the symmetry and topology meet each other which offer the stage of rich physics. In this review, we discuss the physics of ABS from the viewpoint of the odd-frequency pairing, the topological bulk-edge correspondence, and the interplay of these two issues. It is described how the symmetry of the pairing and topological indices determines the absence/presence of the ZEABS, its energy dispersion, and properties as the Majorana fermions.

91 pages, 38 figures, Review article, references added

References in corpus (64)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Scanning tunneling spectroscopy of high-temperature superconductors
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Topological Defects and Gapless Modes in Insulators and Superconductors
• A spin triplet supercurrent through the half-metallic ferromagnet CrO2
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• 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 quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Observation of topological order in a Superconducting doped topological insulator (based on the Bi2Se3 class)
• Helical Metal Inside a Topological Band Insulator
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Topology of Andreev Bound States with Flat Dispersion
• Bulk superconducting phase with a full energy gap in the doped topological insulator Cu_xBi_2Se_3
• Observation of half-height magnetization steps in Sr2RuO4
• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Theory of the proximity effect in junctions with unconventional superconductors
• Search for Majorana fermions in multiband semiconducting nanowires
• Topological spin-current in non-centrosymmetric superconductors
• Electron Correlation and Pairing States in Superconductors without Inversion Symmetry
• Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
• Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures
• Odd-frequency pairing in normal metal/superconductor junctions
• Probability distribution of Majorana end-state energies in disordered wires
• Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Edge states of Sr${}_2$RuO${}_4$ detected by in-plane tunneling spectroscopy
• Anomalous Andreev bound state in non-centrosymmetric superconductors
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• Majorana Fermions in Nodal Superconductors: Gapless Topological Phase
• Manifestation of the odd-frequency spin-triplet pairing state in diffusive ferromagnet / superconductor junctions
• Surface bound states and spin currents in non-centrosymmetric superconductors
• Anomalous Josephson effect in p-wave dirty junctions
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Topologically protected flat zero-energy surface bands in non-centrosymmetric superconductors
• Andreev bound states and tunneling characteristics of a non-centrosymmetric superconductor
• Topological Order and Non-Abelian Statistics in Noncentrosymmetric s-Wave Superconductors
• Pairing symmetry conversion by spin-active interfaces in superconducting junctions
• Spectroscopic Evidence for Multiple Order Parameter Components in the Heavy Fermion Superconductor CeCoIn_5
• Surface spectral function in the superconducting state of a topological insulator
• Conductance Spectroscopy of Spin-triplet Superconductors
• Role of the Majorana Fermion and the Edge Mode in Chiral Superfluidity near a p-Wave Feshbach Resonance
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Surface Majorana Cone of the Superfluid ${}^3$He B Phase
• On stability of odd-frequency superconducting state
• Majorana surface states of superfluid 3He A- and B-phases in a slab
• Quantum impurity spin in Majorana edge fermions
• Theory of pairing symmetry inside the Abrikosov vortex core
• Model for Vortex-core tunneling spectroscopy of chiral p-wave superconductors via odd-frequency pairing states
• Surface Specific Heat of ${}^3$He and Andreev Bound States
• Andreev spectroscopy and surface density of states for a three-dimensional time-reversal invariant topological superconductor
• Long-range odd triplet superconductivity in SF structures with Neel walls
• Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall
• Tunneling between Two Helical Superconductors via Majorana Edge Channels
• Stability of half quantum vortex in rotating superfluid 3He-A between parallel plates
• Majorana edge modes of superfluid 3He A-phase in a slab
• Z${}_2$ index theorem for Majorana zero modes in a class D topological superconductor
• Identifying the odd-frequency superconducting state by a field-induced Josephson effect

Cited by in corpus (458)

• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological Insulator Materials
• Topological superconductors: a review
• Spin-polarized supercurrents for spintronics: a review of current progress
• Topology of crystalline insulators and superconductors
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• Monolayer Topological Insulators: Silicene, Germanene and Stanene
• Topological semi-metals with line nodes and drumhead surface states
• Majorana Fermions and Topology in Superconductors
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Line-Node Dirac Semimetal and Topological Insulating Phase in Noncentrosymmetric Pnictides CaAgX (X = P, As)
• Odd-frequency superconductivity
• Topological superconductivity in bilayer Rashba system
• Two-dimensional topological superconductivity in Pb/Co/Si(111)
• Two-dimensional p-wave superconducting states with magnetic moments on a conventional s-wave superconductor
• Signature of Dispersing 1D Majorana Channels in an Iron-based Superconductor
• Topological surface states in nodal superconductors
• Unconventional Superconductivity at Mesoscopic Point-contacts on the 3-Dimensional Dirac Semi-metal Cd${}_3$As${}_2$
• Topological superconductivity in Dirac semimetals
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Selective Equal-Spin Andreev Reflections Induced by Majorana Fermions
• Altermagnetic Routes to Majorana Modes in Zero Net Magnetization
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to Sr2RuO4
• Topologically protected surface states in a centrosymmetric superconductor beta-PdBi2
• Emergent electromagnetism in solids
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Magneto-Electric Effect in Three-dimensional Coupled Zigzag Chains
• Tunneling Conductance and Surface States Transition in Superconducting Topological Insulators
• Odd-frequency superconducting pairing in multi-band superconductors
• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor
• General Boundary Conditions for Quasiclassical Theory of Superconductivity in the Diffusive Limit: Application to Strongly Spin-polarized Systems
• Recent progress on superconductors with time-reversal symmetry breaking
• Majorana nanowires for topological quantum computation
• Topological Blount's theorem of odd-parity superconductors
• p-wave triggered superconductivity in single layer graphene on an electron-doped oxide superconductor
• Theory of diode effect in d-wave superconductor junctions on the surface of topological insulator
• Crossed surface flat bands of Weyl semimetal superconductors
• Topological Phase Transition without Gap Closing
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Odd-frequency superconducting pairing in one-dimensional systems
• Spin-helical transport in normal and superconducting topological insulators
• Topological states on fractal lattices
• Odd-frequency superconducting pairing in topological insulators
• Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism
• Decoherence of Majorana qubits by noisy gates
• Theory of Majorana zero modes in unconventional superconductors
• Superconducting proximity effect in three-dimensional topological insulators in the presence of a magnetic field
• Odd-Frequency Triplet Superconductivity at the Helical Edge of a Toplogical Insulator
• Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions
• Odd-frequency superconducting states with different types of Meissner response: Problem of coexistence
• Nonsymmorphic Weyl superconductivity in UPt_3 based on E_2u representation
• Superconductivity in doped Dirac semimetals
• Evidence of nodes in the order parameter of the superconducting doped topological insulator Nb${}_x$Bi${}_2$Se${}_3$ via penetration depth measurements
• Majorana qubits in topological insulator nanoribbon architecture
• Topological indices, defects and Majorana fermion in chiral superconductors
• Mesoscopic superconductivity and high spin polarization coexisting at metallic point contacts on the Weyl semimetal TaAs
• Giant thermoelectric effects in a proximity-coupled superconductor-ferromagnet device
• Majorana Fermions and Multiple Topological Phase Transition in Kitaev Ladder Topological Superconductors
• Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor
• Majorana Braiding Dynamics on Nanowires
• Topological Weyl Superconductor to Diffusive Thermal Hall Metal Crossover in the B-Phase of UPt${}_3$
• Superconducting phenomena in systems with unconventional magnets
• Spherical topological insulator
• Odd-frequency Cooper pairs in two-band superconductors and their magnetic response
• Enhancing the Josephson diode effect with Majorana bound states
• A new superconductor derived from topological insulator heterostructure
• Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators
• Topological crystalline superconductivity in locally noncentrosymmetric CeRh${}_2$As${}_2$
• $\phi$ Josephson junction induced by altermagnetism
• The Role of Odd-Frequency Pairing in Multiband Superconductors
• Superconductivity in magnetic multipole states
• Spin Triplet Superconductivity in Sr2RuO4 due to Orbital and Spin Fluctuations: Analysis by Two-Dimensional Renormalization Group Theory
• Andreev bound states and current-phase relations in three-dimensional topological insulators
• Spin-triplet superconductivity in Sr2RuO4 due to orbital and spin fluctuations: Analyses by two-dimensional renormalization group theory and self-consistent vertex-correction method
• Superconducting proximity effect and Majorana flat bands in the surface of a Weyl semimetal
• Topological Crystalline Superconductivity in Locally Non-centrosymmetric Multilayer Superconductors
• Majorana bound states in semiconducting nanostructures
• Proximity induced superconductivity in Weyl semi-metals
• Topologically stable gapless phases in nonsymmorphic superconductors
• Odd-frequency superconducting pairing in junctions with Rashba spin-orbit coupling
• Bulk electronic state of superconducting topological insulator
• Theory of time reversal topological superconductivity in double Rashba wires -- symmetries of Cooper pair and Andreev bound states
• Conductance signatures of odd-frequency superconductivity in quantum spin Hall systems using a quantum point contact
• Band hybridization induced odd-frequency pairing in multiband superconductors
• Superconductivity of Composite Particles in Two-Channel Kondo Lattice
• Axionic superconductivity in three dimensional doped narrow gap semiconductors
• Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability
• Josephson and proximity effects on the surface of a topological insulator
• Strain-sensitive superconductivity in kagome metals KV${}_3$Sb${}_5$ and CsV${}_3$Sb${}_5$ probed by point-contact spectroscopy
• Theory of Tunneling Spectroscopy in Unconventional $p$-wave Magnet-Superconductor Hybrid Structures
• Threefold enhancement of superconductivity and the role of field-induced odd-frequency pairing in epitaxial aluminum films near the 2D limit
• Josephson effect and odd-frequency pairing in superconducting junctions with unconventional magnets
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Topological Crystalline Materials of $J=3/2$ Electrons: Antiperovskites, Dirac points, and High Winding Topological Superconductivity
• Tunable hybridization of Majorana bound states at the quantum spin Hall edge
• Exceptional odd-frequency pairing in non-Hermitian superconducting systems
• Möbius topological superconductivity in UPt${}_3$
• Magnetic field-induced "mirage" gap in an Ising superconductor
• Edge currents as a signature of flat bands in topological superconductors
• Spontaneous edge current in a small chiral superconductor with a rough surface
• Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field
• Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate
• Odd-frequency pair in topological superconductivity of 1D magnetic chain
• The Majorana STM as a perfect detector of odd-frequency superconductivity
• Parity-Mixed Superconductivity in Locally Non-centrosymmetric System
• Fragile surface zero-energy flat bands in three-dimensional chiral superconductors
• Superconducting doped topological materials
• Reentrant topological transitions in a quantum wire/superconductor system with quasiperiodic lattice modulation
• Zero-energy bound states in the high-temperature superconductors at the two-dimensional limit
• Odd-frequency superconductivity in a nanowire coupled to Majorana zero modes
• Observation of triplet superconductivity in CoSi${}_2$/TiSi${}_2$ heterostructures
• Electric Octupole Order in Bilayer Ruthenate Sr${}_3$Ru${}_2$O${}_7$
• Even-odd parity transition in strongly correlated locally noncentrosymmetric superconductors : An application to CeRh${}_2$As${}_2$
• Pairing Obstructions in Topological Superconductors
• Unveiling odd-frequency pairing around a magnetic impurity in a superconductor
• Scanning tunneling spectroscopy of layers of superconducting 2H-TaSe${}_{\text{2}}$: Evidence for a zero bias anomaly in single layers
• Anomalous suppression of the superfluid density in the CuxBi2Se3 superconductor upon progressive Cu intercalation
• Odd-frequency pairing and Kerr effect in the heavy-fermion superconductor UPt${}_3$
• Double helix nodal line superconductor
• Suppression of surface p-wave superconductivity in disordered topological insulators
• Inter-orbital topological superconductivity in spin-orbit coupled superconductors with inversion symmetry breaking
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Tilting of the magnetic field in Majorana nanowires: critical angle and zero-energy differential conductance
• Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality
• Mean-field description of odd-frequency superconductivity with staggered ordering vector
• Paramagnetically induced gapful topological superconductors
• Superconductivity in spin-$3/2$ systems: symmetry classification, odd-frequency pairs, and Bogoliubov Fermi surfaces
• Surface electronic state of superconducting topological crystalline insulator
• General framework for transport in spin-orbit-coupled superconducting heterostructures: Nonuniform spin-orbit coupling and spin-orbit-active interfaces
• General conditions for proximity-induced odd-frequency superconductivity in two-dimensional electronic systems
• Theory of surface Andreev bound states and tunneling spectroscopy in three-dimensional chiral superconductors
• Edge Current due to Majorana Fermions in Superfluid ${}^3$He A- and B-Phases
• Odd-frequency Superconductivity in Driven Systems
• Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
• Odd frequency pairing of interacting Majorana fermions
• Unconventional proximity-induced superconductivity in bilayer systems
• From fractional solitons to Majorana fermions in a paradigmatic model of topological superconductivity
• Classification of pair symmetries in superconductors with unconventional magnetism
• Anomalous interference in Aharonov-Bohm rings with two Majorana bound states
• Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections
• Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-T_c superconductors
• Electrically tunable topological superconductivity and Majorana fermions in two dimensions
• Superfluid 3He in a restricted geometry with a perpendicular magnetic field
• Magnetoelectric Andreev effect due to proximity-induced non-unitary triplet superconductivity in helical metals
• Lifetime of Majorana qubits in Rashba nanowires with non-uniform chemical potential
• Field-free platform for topological zero-energy mode in superconductors LiFeAs and PbTaSe${}_2$
• Microscopic theory of tunneling spectroscopy in Sr${}_2$RuO${}_4$
• Anomalous surface states at interfaces in p-wave superconductors
• Odd-frequency pairing and proximity effect in Kitaev chain systems including topological critical point
• Theory of quasiparticle scattering interference on the surface of topological superconductors
• Transport signatures of superconducting hybrids with mixed singlet and chiral triplet states
• The Josephson current in Fe-based superconducting junctions: theory and experiment
• Possible structural origin of superconductivity in Sr-doped Bi2Se3
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Robustness of Spin-Triplet Pairing and Singlet-Triplet Pairing Crossover in Superconductor/Ferromagnet Hybrids
• Tunneling spectroscopy of topological superconductors
• Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications
• Josephson current signatures of the Majorana flat bands on the surface of time-reversal-invariant Weyl and Dirac semimetals
• Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides
• Anisotropic magnetic responses of topological crystalline superconductors
• Majorana multipole response of topological superconductors
• Coexistence of Even- and Odd-Frequency Superconductivities Under Broken Time-Reversal Symmetry
• All-electrical generation and control of odd-frequency s-wave Cooper pairs in double quantum dots
• Odd-frequency superconducting pairing in Kitaev-based junctions
• Odd-frequency Superconductivity Revealed by Thermopower
• Influence of the impurity scattering on charge transport in unconventional superconductor junctions
• Degeneracy lifting of Majorana bound states due to electron-phonon interactions
• Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization
• Floquet engineering bulk odd-frequency superconducting pairs
• Majorana fermion exchange in strictly one dimensional structures
• Super-Andreev reflection and longitudinal shift of pseudospin-one fermions
• ${}^3{P}_2$ Superfluids Are Topological
• Odd-frequency pairing in (TMTSF)2ClO4
• Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-
• Pair symmetry conversion in driven multiband superconductors
• High-Temperature Majorana Fermions in Magnet-Superconductor Hybrid Systems
• Quasiclassical Eilenberger theory of the topological proximity effect in a superconducting nanowire
• Current fluctuations in unconventional superconductor junctions with impurity scattering
• Probing the superconducting gap structure in the noncentrosymmetric topological superconductor ZrRuAs
• Interplay of Magnetism and Topological Superconductivity in Bilayer Kagome Metals
• Quasi-classical theory of tunneling spectroscopy in superconducting topological insulator
• Spin-orbit coupled superconductivity: Rashba-Hubbard model on the square lattice
• Consequences of bulk odd-frequency superconducting states for the classification of Cooper pairs
• Suppression of odd-frequency pairing by phase-disorder in a nanowire coupled to Majorana zero modes
• Zeeman field induced topological phase transitions in triplet superconductors
• Optical Responses of Chiral Majorana Edge States in Two-Dimensional Topological Superconductors
• Superconductivity in the nonsymmorphic line-nodal compound CaSb${}_2$
• Multi-component order parameter superconductivity of Sr${}_2$RuO${}_4$ revealed by topological junctions
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Orientation-dependent transport in junctions formed by $d$-wave altermagnets and $d$-wave superconductors
• Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model
• Odd-frequency pairing effect on the superfluid density and the Pauli spin susceptibility in spatially nonuniform spin-singlet superconductors
• Electronic multipoles and multiplet pairs induced from Pomeranchuk and Cooper instabilities of Bogoliubov Fermi surfaces
• Anomalous Josephson current in superconducting topological insulator
• Finite bulk Josephson currents and chirality blockade removal from inter-orbital pairing in magnetic Weyl semimetals
• Observability of surface Andreev bound states in a topological insulator in proximity to an s-wave superconductor
• Disorder-robust $p$-wave pairing with odd frequency dependence in normal metal-conventional superconductor junctions
• Josephson Diode Effect in Topological Superconductor
• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• Theory of tunneling spectroscopy for chiral topological superconductors
• Inversion symmetry of Josephson current as test of chiral domain wall motion in Sr${}_2$RuO${}_4$
• Probing vortex Majorana fermions and topology in semiconductor-superconductor heterostructures
• Topological D+p-wave superconductivity in Rashba systems
• Tunneling spectroscopy and Josephson current of superconductor-ferromagnet hybrids on the surface of a 3D TI
• Subgap states in two dimensional spectroscopy of unconventional superconductors using graphene
• Theory of proximity effect in two-dimensional unconventional superconductor with Rashba spin-orbit interaction
• Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
• Magnetic Intragap States and Mixed Parity Pairing at the Edge of Spin-Triplet Superconductors
• Phase-tunable electron transport assisted by odd-frequency Cooper pairs in topological Josephson junctions
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Odd-frequency Cooper pair amplitude around a vortex core in a chiral p-wave superconductor in the quantum limit
• Topological Crystalline Superconductivity in Dirac Semimetal Phase of Iron-based Superconductors
• Quantum transport theory for unconventional magnets: Interplay of altermagnetism and p-wave magnetism with superconductivity
• Odd-frequency pair density wave in the Kitaev-Kondo lattice model
• Large Josephson current in Weyl nodal loop semimetals due to odd-frequency superconductivity
• Generation of spin-triplet Cooper pairs via a canted antiferromagnet
• Interference of Majorana fermions in NS junctions
• Josephson effect in a multi-orbital model for Sr${}_2$RuO${}_4$
• Helical spin texture of surface states in topological superconductors
• S-wave Superconductivity in the Dirac Line-nodal Material CaSb2
• Strong-Coupling Superconductivity with Mixed Even- and Odd-Frequency Pairing
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• New types of topological superconductors under local magnetic symmetries
• Effect of Fermi surface evolution on superconducting gap in superconducting topological insulator
• Novel anisotropic spin singlet pairings in Cu${}_x$Bi${}_2$Se${}_3$ and Bi${}_2$Te${}_3$
• Generalization of spectral bulk-boundary correspondence
• Spin triplet superconducting proximity effect in a ferromagnetic semiconductor
• Interplay of finite-energy and finite-momentum superconducting pairing
• Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems
• Quantum geometry encoded to pair potentials
• Non-Hermitian second-order topological superconductors
• Pairing symmetry of superconductivity coexisting with antiferromagnetism
• Topological superconductivity enhanced by exceptional points
• Emergent Odd-Frequency Superconducting Order Parameter near Boundaries in Unconventional Superconductors
• Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry
• Topological states in normal and superconducting $p$-wave chains
• Entanglement measures of Majorana bound states
• Odd-frequency pairing inherent in Bogoliubov Fermi liquid
• Majorana multipole response: General theory and application to wallpaper groups
• Odd-frequency pair density wave correlations in underdoped cuprates
• Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model
• Superconducting proximity in three dimensional Dirac materials: odd-frequency, pseudoscalar, pseudovector and tensor-valued superconducting orders
• Dislocation Majorana zero modes in perovskite oxide 2DEG
• Localization and oscillations of Majorana fermions in a two-dimensional electron gas coupled with $d$-wave superconductors
• Laser-induced topological $s$-wave superconductivity in bilayer transition metal dichalcogenides
• Gapped superconductivity with all symmetries in InSb (110) quantum wells in proximity to s-wave superconductor in Fulde-Ferrell-Larkin-Ovchinnikov phase or with a supercurrent
• Anomalous Proximity Effect of Planer Topological Josephson Junctions
• Possible odd-frequency Amperean magnon-mediated superconductivity in topological insulator -- ferromagnetic insulator bilayer
• Effects of spin orbit coupling in superconducting proximity devices -- application to $\mathrm{CoS}{\mathrm{i}}_2/TiS{\mathrm{i}}_2$ heterostructures
• Chirality polarizations and spectral bulk-boundary correspondence
• Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems
• Domain walls in a chiral d-wave superconductor on the honeycomb lattice
• Coreless vortices as direct signature of chiral $d$-wave superconductivity
• Effect of a spin-active interface on proximity-induced superconductivity in topological insulators
• Observability of surface currents in p-wave superconductors
• Odd-frequency Berezinskii superconductivity in Dirac semimetals
• Topological Larkin-Ovchinnikov phase and Majorana zero mode chain in bilayer superconducting topological insulator films
• Signature of a topological phase transition in long SN junctions in the spin-polarized density of states
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Nonlocal conductance reveals helical superconductors
• Josephson diode effect with Andreev and Majorana bound states
• Topological flat bands in optical checkerboard-like lattices
• Fermi surface effect on spontaneous breaking of time-reversal symmetry in unconventional superconducting films
• Thermoelectric detection of Andreev states in unconventional superconductors
• Higher-order topological and nodal superconducting transition-metal sulfides MS (M = Nb and Ta)
• Controllable odd-frequency Cooper pairs in multi-superconductor Josephson junctions
• Tunneling and Josephson effects in odd-frequency superconductor junctions: A study on multi-channel Kondo chain
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Non-Hermitian minimal Kitaev chains
• Exciting odd frequency equal-spin-triplet correlations at metal-superconductor interfaces
• Quasiparticle on Bogoliubov Fermi Surface and Odd-Frequency Cooper Pair
• Edge instabilities of topological superconductors
• Theory of proximity effect in $s+p$-wave superconductor junctions
• Site-selective NMR for odd-frequency Cooper pairs around vortex in chiral p-wave superconductors
• Floquet engineering spin triplet states in unconventional magnets
• Superconducting pairing symmetry on the extended Hubbard model in the presence of the Rashba-type spin-orbit coupling
• Theory of pair density wave on a quasi-one-dimensional lattice in the Hubbard model
• Proximity-Induced Mixed Odd and Even Frequency Pairings in Monolayer NbSe${}_2$
• Emergent pair symmetries in systems with poor man's Majorana modes
• Two-impurity helical Majorana problem
• Effective low energy theory for surface Andreev bound states of superconducting phases in generalized Bernevig-Hughes-Zhang models
• Symmetry analysis of odd- and even-frequency superconducting gap symmetries for time-reversal symmetric interactions
• Odd-frequency superconductivity in dilute magnetic superconductors
• Spin susceptibility for orbital-singlet Cooper pair in the three-dimensional Sr${}_2$RuO${}_4$ superconductor
• Oscillating paramagnetic Meissner effect and Berezinskii-Kosterlitz-Thouless transition in $B{i}_{2}S{r}_{2}CaC{u}_2{O}_{8+\delta }$ monolayer
• Crossed Andreev reflection in topological insulator nanowire T-junctions
• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• Appearance of flat surface bands in three-dimensional topological insulators in a ferromagnetic exchange field
• Induced odd-frequency superconducting state in vertex-corrected Eliashberg theory
• Planar Josephson Hall effect in topological Josephson junctions
• Complete $T_c$ suppression and Néel triplets-mediated exchange in antiferromagnet-superconductor-antiferromagnet trilayers
• Transport and noise properties of a normal metal-superconductor-normal metal junction with mixed singlet and chiral triplet pairings
• Gapless odd-frequency superconductivity induced by the Sachdev-Ye-Kitaev model
• Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping
• Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials
• Strong anomalous proximity effect from spin-singlet superconductors
• Effects of the phase coherence on the local density of states in superconducting proximity structures
• Thermodynamics in topological Josephson junctions
• Dual topological superconducting states in the layered titanium-based oxypnictide superconductor BaTi${}_2$Sb${}_2$O
• Edge-induced pairing states in a Josephson junction through a spin-polarized quantum anomalous Hall insulator
• Influence of diffuse surface scattering on the stability of superconducting phases with spontaneous surface current generated by Andreev bound states
• The invisible Majorana bound state at the helical edge
• Topological Defects in Systems with Two Competing Order Parameters: Application to Superconductors with Charge- and Spin-Density Waves
• Local impedance on a rough surface of a chiral $p$-wave superconductor
• Enhancing triplet superconductivity by the proximity to a singlet superconductor in oxide heterostructures
• Chiral current-phase relation of topological Josephson junctions: A signature of the $4\pi$-periodic Josephson effect
• Effect of disorder on Majorana localization in topological superconductors: a quasiclassical approach
• Quasiparticle interference as a direct experimental probe of bulk odd-frequency superconducting pairing
• Generation of polarized spin-triplet Cooper pairings by magnetic barriers in superconducting junctions
• Odd-frequency superconductivity induced by non-magnetic impurities
• Topological signatures of the coexistence of antiferromagnetism and odd-parity spin-triplet superconductivity
• Andreev reflection in Euler materials
• Local density of states in two-dimensional topological superconductors under a magnetic field: signature of an exterior Majorana bound state
• Surface density of states and tunneling spectroscopy of a spin-3/2 superconductor with Bogoliubov Fermi Surfaces
• Pairing mechanism of unconventional superconductivity in doped Kane-Mele model
• Josephson current in a normal-metal nanowire coupled to superconductor/ferromagnet/superconductor junction
• Quasiparticle density of states and triplet correlations in superconductor/ferromagnetic-insulator structures across a sharp domain wall
• Emergence of strongly correlated electronic states driven by the Andreev bound state in d-wave superconductors
• Generation of odd-frequency surface superconductivity with spontaneous spin current due to the zero-energy Andreev bound state
• Anomalous inverse proximity effect in unconventional-superconductor junctions
• Reentrant superconductivity in proximity to a topological insulator
• Anomalous Surface Impedance in a Normal-metal/Superconductor Junction with a Spin-active Interface
• Spin-triplet $f$-wave symmetry in superconducting monolayer $Mo{S}_2$
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Electric Multipoles of Double Majorana Kramers Pairs
• Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors
• Signatures of odd-frequency pairing in the Josephson junction current noise
• Majorana fermions in $T$-shaped semiconductor nanostructures
• An odd-frequency Cooper pair around a magnetic impurity
• Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets
• Odd-frequency pairing due to Majorana and trivial Andreev bound states
• Tunneling conductance in superconducting junctions with $p$-wave unconventional magnets breaking time-reversal symmetry
• Spectroscopic and optical response of odd-frequency superconductors
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Control of Edge Currents at a Ferromagnet - Triplet Superconductor Interface by Multiple Helical Majorana Modes
• Direct detection of odd-frequency superconductivity via time- and angle-resolved photoelectron fluctuation spectroscopy
• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
• Proximity effect in superconductor/conical magnet heterostructures
• Odd-frequency pairing in a superconductor coupled to two parallel nanowires
• Anisotropic paramagnetic response of topological Majorana surface states in the superconductor ${\text{UTe}}_2$
• Disorder-dependent superconducting pairing symmetry in doped graphene
• Spin susceptibility of Andreev bound states
• Unusual Superconducting Proximity Effect in Magnetically Doped Topological Josephson Junctions
• Odd-frequency pairing in a nonunitary p-wave superconductor with multiple Majorana fermions
• Tip-induced Superconductivity
• Charge and Spin Supercurrents in Magnetic Josephson Junctions with Spin Filters and Domain Walls
• Long range $p$-wave proximity effect into a disordered metal
• Andreev spectroscopy of the triplet superconductivity state in Bi/Ni bilayer system
• Interface currents and magnetization in singlet-triplet superconducting heterostructures: Role of chiral and helical domains
• Triplet superconductivity and proximity effect induced by Bloch and Néel domain walls
• Identifying Majorana bound states at quantum spin Hall edges using a metallic probe
• Odd-frequency Pairing in the Edge States of Superconducting Pnictides in the Coexistence Phase with Antiferromagnetism
• Ferroelectricity-induced multiorbital odd-frequency superconductivity in SrTiO${}_3$
• Impurity effect on Bogoliubov Fermi surfaces: Analysis based on iron-based superconductors
• Proximity effect of time-reversal symmetry broken non-centrosymmetric superconductors
• Effects of Weak and Strong Scatterers on the Spectra of Vortex Andreev Bound States in Two-Dimensional Chiral p-wave Superconductors
• Symmetry analysis of transport properties in helical superconductor junctions
• Surface State of Inter-orbital Pairing State in Sr${}_2$RuO${}_4$ Superconductor
• Josephson effect of superconductors with $J=3/2$ electrons
• Anomalous proximity effect under Andreev and Majorana bound states
• Quantum Pairing Time Orders
• Majorana modes in striped two-dimensional inhomogeneous topological superconductors
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Probing the magnetoelectric effect in noncentrosymmetric superconductors by equal-spin Andreev tunneling
• Topology of superconductors beyond mean-field theory
• Perfect Zitterbewegung oscillations in the Kitaev chain system
• Spin conductance in SNN junctions with non-centrosymmetric superconductors
• Discontinuous Transition to Superconducting Phase
• Coexistence of Chiral Majorana Edge States and Bogoliubov Fermi Surfaces in Two-Dimensional Nonsymmorphic Dirac Semimetal/Superconductor Heterostructures
• Majorana fermions in semiconductor nanostructures with two wires connected through ring
• Spin Susceptibility of a J=3/2 Superconductor
• Odd-frequency pairing and time-reversal symmetry breaking for repulsive interactions
• Tomasch Oscillations as Above-Gap Signature of Topological Superconductivity
• Impact of impurity scattering on odd-frequency spin-triplet pairing near the edge of the Kitaev chain
• Effect of transport-induced charge inhomogeneity on point-contact Andreev reflection spectra at ferromagnet-superconductor interfaces
• Theory of Josephson Current on a Magnetically Doped Topological Insulator
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Majorana multipole response with magnetic point group symmetry
• Predicting topological invariants and unconventional superconducting pairing from density of states and machine learning
• Majorana bound states in d-wave superconductor planar Josephson junction
• Enhanced zero-bias conductance peak and splitting at mesoscopic interfaces between an $s$-wave superconductor and a 3D Dirac semimetal
• Mixing of odd- and even-frequency pairings in strongly correlated electron systems under magnetic field
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• Engineering Frequency-dependent Superfluidity in Bose-Fermi Mixtures
• Hall effect of ferro/antiferromagnetic wallpaper fermions
• Representation-protected topology of spin-singlet $s$-wave superconductors
• Reciprocal and nonreciprocal paraconductivity in bilayer multiphase superconductors
• Ever-present Majorana bound state in a generic one-dimensional superconductor with odd number of Fermi surfaces
• Appearance of Odd-Frequency Superconductivity in a Relativistic Scenario
• Non-Hermitian Josephson junctions with four Majorana zero modes
• Engineering subgap states in superconductors by the symmetry of altermagnetism
• Quantum spin Hall insulator in proximity with a superconductor: Transition to the Fulde-Ferrell-Larkin-Ovchinnikov state driven by a Zeeman field
• Vortex supercurrent inversion by frequency-symmetry conversion of Cooper pairs
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Pairing properties of an odd-frequency superfluid Fermi gas
• Fluctuation-induced odd-frequency spin-triplet pairing in disordered electron liquid
• Majorana Spin Current Generation by Dynamic Strain
• Euler--Chern Correspondence via Topological Superconductivity
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Topological phase transitions in superconductors with chiral symmetry
• Jackiw-Rebbi-type bound state carrying fractional fermion parity
• Theory of tunneling spectroscopy in a superconducting topological insulator
• Multi-locational Majorana Zero Modes
• Surface induced odd-frequency spin-triplet superconductivity as a veritable signature of Majorana bound states
• P-wave pairing near a spin-split Josephson junction
• Impurity bands, line-nodes, and anomalous thermal Hall effect in Weyl superconductors
• Magnetic edge fields in UTe${}_2$ near zero background fields
• Floquet-Nambu theory of electron quantum optics with superconductors
• Majorana polarization in disordered heterostructures
• Magnon-mediated superconductivity on ferromagnetic wallpaper fermions
• Enhancement of Josephson Supercurrent in a $\pi$-Junction state by Chiral Antiferromagnetism
• Quasiparticle spectrum in mesoscopic superconducting junctions with weak magnetization
• Majorana edge states and topological properties in 1D/2D Rashba semiconductor proximity coupled to iron-based superconductor
• Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge
• Vortex bound state of Kondo lattice coupled to compensated metal
• Signatures of Long-Range Spin-Triplet Component in Andreev Interferometer
• Magnetic Susceptibility of Dirac Fermions, Bi-Sb Alloys, Interacting Bloch Fermions, Dilute Nonmagnetic Alloys, and Kondo Alloys
• Emergence of Non-Axisymmetric Vortex in Strong-Coupling Chiral p-Wave Superconductor
• The Josephson effect in Fibonacci superconductors
• Yu-Shiba-Rusinov bound states boost odd-frequency superconductivity
• Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction
• Generic Weyl phase in the vortex state of quasi-two-dimensional chiral superconductors
• Theory of Tunneling Effect in 1D AIII-class Topological Insulator (Nanowire) Proximity Coupled with a Superconductor
• Particle-hole spectral asymmetry at the edge of multiorbital noncentrosymmetric superconductors
• $\eta$-pairing on bipartite and non-bipartite lattices
• Localized interfacial Phonon Modes at the Electronic Axion Domain Wall
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors
• Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
• Equal contribution of even and odd frequency pairing to transport across normal metal-superconductor junctions
• Tunneling Magnetoresistance in Junctions Composed of Ferromagnets and Time-Reversal Invariant Topological Superconductors
• Multiple phases in K2Cr3As3: a playground for manipulating topological superconductivity
• Fractional spin Josephson effect in topological spin superconductors
• Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes
• Nonequilibrium Green's function approach to multi-band Cooper-pair transport: linear magnetoresistance effect due to nonunitary superconductivity
• Identification of odd-frequency superconducting pairing in Josephson junctions
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• Spin injection and spin relaxation in odd-frequency superconductors
• Low-temperature anomaly and anisotropy of critical magnetic fields in transition-metal dichalcogenide superconductors
• Quantum theory for edge current and noise in two-dimensional topological superconductors
• Phase Thermalization: from Fermi Liquid to Incoherent Metal
• Influence of Magnetic Order on Proximity-Induced Superconductivity in Mn Layers on Nb(110) from First Principles
• Majorana modes in graphene strips: polarization, wavefunctions, disorder, and Andreev states
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Spin-Valley Locking and Pure Spin-Triplet Superconductivity in Noncollinear Antiferromagnets Proximitized to Conventional Superconductors
• Eight-fold classification of superconducting orders
• Topological superconductivity in helical crystals
• Entanglement dynamics in minimal Kitaev chains
• Gaplessness from disorder and quantum geometry in gapped superconductors
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors