Majorana Fermions and Topology in Superconductors

Abstract

Topological superconductors are novel classes of quantum condensed phases, characterized by topologically nontrivial structures of Cooper pairing states. On the surfaces of samples and in vortex cores of topological superconductors, Majorana fermions, which are particles identified with their own anti-particles, appear as Bogoliubov quasiparticles. The existence and stability of Majorana fermions are ensured by bulk topological invariants constrained by the symmetries of the systems. Majorana fermions in topological superconductors obey a new type of quantum statistics referred to as non-Abelian statistics, which is distinct from bose and fermi statistics, and can be utilized for application to topological quantum computation. Also, Majorana fermions give rise to various exotic phenomena such as "fractionalization", non-local correlation, and "teleportation". A pedagogical review of these subjects is presented. We also discuss interaction effects on topological classification of superconductors, and the basic properties of Weyl superconductors.

81 pages, 12 figures, an invited review paper of J. Phys. Soc. Jpn

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• Anomalous Andreev bound state in non-centrosymmetric superconductors
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Thermal Hall Effect and Geometry with Torsion
• Low-energy effective theory in the bulk for transport in a topological phase
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• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Topological Blount's theorem of odd-parity superconductors
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• Topological Order and Non-Abelian Statistics in Noncentrosymmetric s-Wave Superconductors
• Testable signatures of quantum non-locality in a two-dimensional chiral p-wave superconductor
• Crossed surface flat bands of Weyl semimetal superconductors
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Surface spectral function in the superconducting state of a topological insulator
• Topological States in a One-Dimensional Fermi Gas with Attractive Interactions
• Shortcuts to nonabelian braiding
• Majorana Braiding Dynamics on Nanowires
• Colossal thermomagnetic response in the exotic superconductor URu2Si2
• To close or not to close: the fate of the superconducting gap across the topological quantum phase transition in Majorana-carrying semiconductor nanowires
• Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state
• Anisotropic magnetic fluctuations in the ferromagnetic superconductor UCoGe studied by angle-resolved ^{59}Co NMR
• Observable Bulk Signatures of Non-Abelian Quantum Hall States
• Quantum impurity spin in Majorana edge fermions
• The Fermi surface and f-valence electron count of UPt3
• Scattering theory of chiral Majorana fermion interferometry
• Odd-frequency pair in topological superconductivity of 1D magnetic chain
• Superconducting doped topological materials
• Studies of the superconducting properties of Sn1-xInxTe (x=0.38 to 0.45) using muon-spin spectroscopy
• Electromagnetic and thermal responses of Z topological insulators and superconductors in odd spatial dimensions
• Detecting Non-Abelian Anyons by Charging Spectroscopy
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Cited by in corpus (280)

• Topological superconductors: a review
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• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Majorana corner modes in a high-temperature platform
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Hunting Majorana Fermions in Kitaev Magnets
• Physical mechanisms for zero-bias conductance peaks in Majorana nanowires
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Unconventional Superconductivity in UTe2
• Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Effects of gate-induced electric fields on semiconductor Majorana nanowires
• Search for non-Abelian Majorana braiding statistics in superconductors
• Insulator-metal transition and topological superconductivity in UTe2 from a first-principles calculation
• Majorana nanowires for topological quantum computation
• Majorana corner modes and tunable patterns in an altermagnet heterostructure
• Distinguishing topological Majorana bound states from trivial Andreev bound states: Proposed tests through differential tunneling conductance spectroscopy
• Type I superconductivity in the Dirac semimetal PdTe2
• Refined symmetry indicators for topological superconductors in all space groups
• Periodic Anderson model for magnetism and superconductivity in UTe2
• Higher-order Topological Mott Insulators
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Generic quantized zero-bias conductance peaks in superconductor-semiconductor hybrid structures
• A perspective on semiconductor-based superconducting qubits
• Theory of Majorana zero modes in unconventional superconductors
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Electron temperature and tunnel coupling dependence of zero-bias and almost-zero-bias conductance peaks in Majorana nanowires
• Superconductivity in doped Dirac semimetals
• Superconducting phenomena in systems with unconventional magnets
• Higher-order topological superconductivity: possible realization in Fermi gases and Sr${}_2$RuO${}_4$
• Topological crystalline superconductivity in locally noncentrosymmetric CeRh${}_2$As${}_2$
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Majorana bound states in semiconducting nanostructures
• Electrical probes of the non-Abelian spin liquid in Kitaev materials
• Braiding Majorana zero modes using quantum dots
• Bulk-edge correspondence of classical diffusion phenomena
• Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals
• Multi-critical Behavior in Topological Phase Transitions
• Square-root topological semimetals
• Unconventional p-wave and finite-momentum superconductivity induced by altermagnetism through the formation of Bogoliubov Fermi surface
• Fusion protocol for Majorana modes in coupled quantum dots
• Spinful topological phases in acoustic crystals with projective PT symmetry
• Laser-induced topological superconductivity in cuprate thin films
• Topological Crystalline Materials of $J=3/2$ Electrons: Antiperovskites, Dirac points, and High Winding Topological Superconductivity
• Symmetry protected line nodes in non-symmorphic magnetic space groups: Applications to UCoGe and UPd${}_2$Al${}_3$
• Detection of second-order topological superconductors by Josephson junctions
• Möbius topological superconductivity in UPt${}_3$
• Fermionized parafermions and symmetry-enriched Majorana modes
• $Z_4$ Topological Superconductivity in UCoGe
• Metamorphosis of Andreev bound states into Majorana bound states in pristine nanowires
• Majorana flat bands, chiral Majorana edge states, and unidirectional Majorana edge states in noncentrosymmetric superconductors
• Valley-dependent Corner States in Honeycomb Photonic Crystal without Inversion Symmetry
• Even-odd parity transition in strongly correlated locally noncentrosymmetric superconductors : An application to CeRh${}_2$As${}_2$
• Universal Majorana thermoelectric noise
• 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
• Experimental Progress on Layered Topological Semimetals
• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Electronic properties of InAs/EuS/Al hybrid nanowires
• Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality
• Chiral singlet superconductivity in the weakly correlated metal LaPt3P
• Majorana-fermion origin of the planar thermal Hall effect in the Kitaev magnet $\alpha$-RuCl${}_3$
• Theory of surface Andreev bound states and tunneling spectroscopy in three-dimensional chiral superconductors
• Majorana Zero Modes Protected by Hopf Invariant in Topologically Trivial Superconductors
• Topological superconductivity from magnetic impurities on monolayer NbSe${}_2$
• Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires
• Time Reversal Symmetry Breaking in the B Phase of the Heavy Fermion Superconductor PrOs${}_4$Sb${}_{12}$
• Recent progress on Majorana in semiconductor-superconductor heterostructures--Engineering and detection
• Fibonacci anyons versus Majorana fermions
• Dynamic Majorana resonances and universal symmetry of nonequilibrium thermoelectric quantum noise
• Spin-triplet superconductivity from quantum-geometry-induced ferromagnetic fluctuation
• Majorana finite frequency nonequilibrium quantum noise
• Majorana multipole response of topological superconductors
• Evolution of topological superconductivity by orbital selective confinement in oxide nanowires
• Nonequilibrium Majorana fluctuations
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• ${}^3{P}_2$ Superfluids Are Topological
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• Weyl-Majorana solenoid
• Majorana entropy revival via tunneling phases
• Superconductivity under pressure in the Dirac semimetal PdTe2
• High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits
• Majorana ensembles with fractional entropy and conductance in nanoscopic systems
• Majorana flat band edge modes of topological gapless phase in 2D Kitaev square lattice
• Negative thermal magnetoresistivity as a signature of chiral anomaly in Weyl superconductors
• Nonlinear optical responses in noncentrosymmetric superconductors
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Conductance feature smearing and anisotropic suppression of induced superconductivity in a Majorana nanowire
• Effects of the electrostatic environment on superlattice Majorana nanowires
• Quantum Transport and Potential of Topological States for Thermoelectricity in Bi${}_2$Te${}_3$ Thin Films
• Mixed type I and type II superconductivity due to intrinsic electronic inhomogeneities in the type II Dirac semimetal PdTe2
• Superconducting islands with semiconductor-nanowire-based topological Josephson junctions
• Superconductivity in the nonsymmorphic line-nodal compound CaSb${}_2$
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• Non-local spin correlation as a signature of Ising anyons trapped in vacancies of the Kitaev spin liquid
• Altermagnetism-Induced Parity Anomaly in Weak Topological Insulators
• Kitaev chain in an alternating quantum dot-Andreev bound state array
• Charge/Spin Supercurrent and the Fulde-Ferrell State Induced by Crystal Deformation in Weyl/Dirac Superconductors
• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• Majorana fermion from Landau quantization in 2D topological superconductors
• Theory of proximity effect in two-dimensional unconventional superconductor with Rashba spin-orbit interaction
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Impurity-induced states in superconducting heterostructures
• Topological Edge States Induced by Zak's Phase in A3B Monolayers
• Quasiparticle gaps in multiprobe Majorana nanowires
• Topological Crystalline Superconductivity in Dirac Semimetal Phase of Iron-based Superconductors
• Majorana-like localized spin density without bound states in topologically trivial spin-orbit coupled nanowires
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly
• Efficient method to compute ${\mathbb{Z}}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• S-wave Superconductivity in the Dirac Line-nodal Material CaSb2
• Majorana bound states in germanium Josephson junctions via phase control
• The improved inverted AlGaAs/GaAs interface: its relevance for high-mobility quantum wells and hybrid systems
• Majorana differential shot noise and its universal thermoelectric crossover
• Low-energy excitations and non-BCS superconductivity in Nb${}_x$-Bi${}_2$Se${}_3$
• Improved effective equation for the Rashba spin-orbit coupling in semiconductor nanowires
• New types of topological superconductors under local magnetic symmetries
• Fano-Andreev effect in T-shape double-quantum-dot in the Kondo regime
• Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor
• Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems
• Spin triplet superconducting proximity effect in a ferromagnetic semiconductor
• Quantum geometry encoded to pair potentials
• Majorana multipole response: General theory and application to wallpaper groups
• Surface state tunneling signatures in two-component superconductor UPt${}_3$
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Rabi and Ramsey oscillations of a Majorana qubit in a quantum dot-superconductor array
• Flux-tunable Kitaev chain in a quantum dot array
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Conductance asymmetries in mesoscopic superconducting devices due to finite bias
• Giant surface Edelstein effect in $d$-wave superconductors
• Dual Majorana universality in thermally induced nonequilibrium
• All-electric spin device operation using the Weyl semimetal, WTe${}_2$, at room temperature
• Topological superconductor in quasi-one-dimensional Tl2-xMo6Se6
• Chirality polarizations and spectral bulk-boundary correspondence
• Protocol for reading out Majorana vortex qubit and testing non-Abelian statistics
• Torsional chiral magnetic effect due to skyrmion textures in a Weyl superfluid ${}^3$He-A
• Engineering Yang-Lee anyons via Majorana bound states
• Josephson diode effect with Andreev and Majorana bound states
• Proposal for measuring the parity anomaly in a topological superconductor ring
• Quarter-quantized thermal Hall effect with parity anomaly
• Review: Observation of Majorana Bound States at a Free Surface of ${}^3$He-B
• Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• 1D Majorana Goldstinos and partial supersymmetry breaking in quantum wires
• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Thermoelectric detection of Andreev states in unconventional superconductors
• Searching for two-dimensional Weyl superconductors in heterostructures
• Paramagnetic effects of j-electron superconductivity and application to UTe2
• Single branch of chiral Majorana modes from doubly degenerate Fermi surfaces
• Non-Hermitian minimal Kitaev chains
• Topological Anomalous Skin Effect in Weyl Superconductors
• Curvature of gap closing features and the extraction of Majorana nanowire parameters
• Bulk superconductivity and non-trivial band topology analysis of Pb2Pd
• Spin, orbital and topological order in models of strongly correlated electrons
• Generic phase diagram for Weyl superconductivity in mirror-symmetric superconductors
• Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Effects of the phase coherence on the local density of states in superconducting proximity structures
• Plasmons in Two-Dimensional Topological Insulators
• Non-thermodynamic nature of the orbital angular momentum in neutral fermionic superfluids
• Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models
• Dual topological superconducting states in the layered titanium-based oxypnictide superconductor BaTi${}_2$Sb${}_2$O
• Identifying non-Abelian anyons with upstream noise
• Local density of states in two-dimensional topological superconductors under a magnetic field: signature of an exterior Majorana bound state
• Intrinsic Anomalous Thermal Hall Effect in the Unconventional Superconductor UTe2
• Searching for Majorana quasiparticles at vortex cores in iron-based superconductors
• Wiedemann-Franz-type relation between shot noise and thermal conduction of Majorana surface states in a three-dimensional topological superconductor
• Visualization by scanning SQUID microscopy of the intermediate state in the superconducting Dirac semimetal PdTe${}_2$
• Spin-Nernst Effect in Time-Reversal-Invariant Topological Superconductors
• Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields
• Nonequilibrium finite frequency resonances in differential quantum noise driven by Majorana interference
• Switchable Non-Hermitian Skin Effect in Bogoliubov Modes
• Optical spin transport theory of spin-1/2 topological Fermi superfluids
• Scaling up a sign-ordered Kitaev chain without magnetic flux control
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• Complete description of fault-tolerant quantum gate operations for topological Majorana qubit systems
• Optimizing the topological properties of stacking semiconductor-ferromagnet-superconductor heterostructures
• Topological multiband s-wave superconductivity in coupled multifold fermions
• Field-driven spatiotemporal manipulation of Majorana zero modes in a Kitaev spin liquid
• Odd-frequency pairing due to Majorana and trivial Andreev bound states
• Superconducting properties of Cu intercalated Bi${}_2$Se${}_3$ studied by Muon Spin Spectroscopy
• Anomalous Coherence Length of Majorana Zero Modes at Vortices in Superconducting Topological Insulators
• Inversion-asymmetric itinerant antiferromagnets by the space group symmetry
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Josephson current via an isolated Majorana zero mode
• Phonon-induced Majorana Qubit Relaxation in Tunnel-Coupled Two-Island Topological Superconductors
• Modern Theory for the Orbital Moment in a Superconductor
• Nonlinear optical responses in superconductors under magnetic fields: quantum geometry and topological superconductivity
• Nodal superconducting gap structure and topological surface states of UTe${}_2$
• Spin Susceptibility of a J=3/2 Superconductor
• Anomalous proximity effect under Andreev and Majorana bound states
• Controllable enhancement of $p$-wave superconductivity via magnetic coupling to a conventional superconductor
• Majorana modes in striped two-dimensional inhomogeneous topological superconductors
• Josephson effect of superconductors with $J=3/2$ electrons
• Enhanced $2\pi$-periodic Aharonov-Bohm Effect as a Signature of Majorana Zero Modes Probed by Nonlocal Measurements
• Spin caloritronics as a probe of nonunitary superconductors
• All-electrical spectroscopy of topological phases in semiconductor-superconductor heterostructures
• Coexistence of Chiral Majorana Edge States and Bogoliubov Fermi Surfaces in Two-Dimensional Nonsymmorphic Dirac Semimetal/Superconductor Heterostructures
• Tunable Majorana corner modes by orbital-dependent exchange interaction in a two-dimensional topological superconductor
• A topological current divider
• Effect of hybridization symmetry on topological phases of odd-parity multiband superconductors
• Discriminant indicator with generalized rotational symmetry
• The Dirac paradox in 1+1 dimensions and its realization with spin-orbit coupled nanowires
• Three-dimensional time reversal invariant topological superconductivity in doped chiral topological semimetals
• Maximal distant entanglement in Kitaev tube
• Majorana multipole response with magnetic point group symmetry
• Anomalous acoustoelectric effect induced by clapping modes in chiral superconductors
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Non-centrosymmetric superconductors on honeycomb lattice
• Superconductor/normal-metal/superconductor junction of topological superconductors revisited: Fractional Josephson current, fermion parity, and oscillating wavefunctions
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• Engineering subgap states in superconductors by the symmetry of altermagnetism
• Representation-protected topology of spin-singlet $s$-wave superconductors
• Reciprocal and nonreciprocal paraconductivity in bilayer multiphase superconductors
• Topological phase transitions in superconductors with chiral symmetry
• Topological Computation by non-Abelian Braiding in Classical Metamaterials
• Two-dimensional flat band on the (011) surface of UTe${}_2$: Implication for STM measurements with a superconducting tip
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Non-Hermitian Josephson junctions with four Majorana zero modes
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Surface step states and Majorana end states in profiled topological insulator thin films
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Fulde-Ferrell state in ferromagnetic chiral superconductor with magnetic domain wall
• Fractionalization of Majorana-Ising-type quasiparticles
• A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System
• Antisymmetric Spin-Orbit Coupling Effect on Kondo-Induced Electric Polarization in a Triangular Triple Quantum Dot
• Giant quantum oscillations in thermal transport in low-density metals via electron absorption of phonons
• Anisotropic superconducting gap probed by ${}^{125}$Te NMR in noncentrosymmetric Sc${}_{6}M$Te${}_2$ ($M$ = Fe, Co)
• Majorana Bound States hallmark in a quantum topological interferometer ring
• Confinement versus interface bound states in spin-orbit coupled nanowires
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Hexagonal warping effect to Majorana zero modes at ends of superconducting vortex line in doped 3D strong topological insulators
• Impurity bands, line-nodes, and anomalous thermal Hall effect in Weyl superconductors
• Fusion Rules of Majorana-Kramer-Pairs in Time-Reversal-Invariant Topological Superconductors
• Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation
• Realizing tunable Fermi level in SnTe by defect control
• Multi-locational Majorana Zero Modes
• Topological zero modes and bounded modes at smooth domain walls: Exact solutions and dualities
• Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge
• Thermoelectric fluctuations of interfering Majorana bound states
• Magnetic fluctuations and anisotropy in UTe2: a multi-orbital study based on GGA+U and RPA
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Laughlin charge pumping from interplay of chiral Dirac and chiral Majorana modes
• Time-dependent Gutzwiller simulation of Floquet topological superconductivity
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors
• Entanglement distribution in fermion model with long-range interaction
• Coalescence of Andreev bound states on the surface of a chiral topological semimetal
• Landau levels and optical conductivity in the mixed state of a generic Weyl superconductor
• Confinement-induced zero-bias peaks in conventional superconductor hybrids
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Euler band topology in superfluids and superconductors
• Multiterminal Josephson junctions with tunable topological properties
• Rashba spin-orbit coupling and artificially engineered topological superconductors
• Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
• Majorana bound states with chiral magnetic textures
• Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes
• Double-twisted surface spectrum from hybridized Majorana Kramers pairs and wallpaper fermions
• Realizing attractive interacting topological surface fermions: A resonating TI- thin film hybrid platform
• Excess photon-assisted noise of Majorana and Andreev bound states
• Quasiparticle Interference of Spin-Triplet Superconductors: Application to UTe${}_2$
• Entanglement dynamics in minimal Kitaev chains
• Ballistic transport in 1D Rashba systems in the context of Majorana nanowires
• Magnetic excitations in the helical Rashba superconductor
• Semiclassical theory for the orbital magnetic moment of superconducting quasiparticles
• Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons
• Revealing universal Majorana fractionalization using differential shot noise and conductance in nonequilibrium states controlled by tunneling phases
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• Electronic structure of UTe${}_2$ under pressure
• Emergent One-Dimensional Helical Channel in Higher-Order Topological Insulators with Step Edges
• Many-body wave function and edge magnetization of an open $p+is$ superconducting chain
• Anisotropic supercurrent suppression and revivals in a graphene-based Josephson junction under in-plane magnetic fields
• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed $s$- and $d$-wave symmetries
• The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm
• Observation of the crossover from quantum fluxoid to half-quantum fluxoid in a chiral superconducting device
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$
• Topological superconductivity in helical crystals
• Influence of Magnetic Field on Surface Andreev Bound States in Superfluid ${}^3$He-B Studied by Mobility of Electron Bubble
• Fluctuation response of a minimal Kitaev chain in nonequilibrium states