Magnetic impurities on the surface of a topological insulator

Abstract

The surface states of a topological insulator are described by an emergent relativistic massless Dirac equation in 2+1 dimensions. In contrast to graphene, there is an odd number of Dirac points, and the electron spin is directly coupled to the momentum. We show that a magnetic impurity opens up a local gap and suppresses the local density of states. Furthermore, the Dirac electronic states mediate an RKKY interaction among the magnetic impurities which is always ferromagnetic, whenever the chemical potential lies near the Dirac point. These effects can be directly measured in STM experiments. We also study the case of quenched disorder through a renormalization group analysis.

5 pages, 2 figures

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• Topological insulators and superconductors
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
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• Experimental demonstration of the topological surface states protected by the time-reversal symmetry
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• A topological insulator surface under strong Coulomb, magnetic and disorder perturbations
• Electronic structure of quantum materials studied by angle-resolved photoemission spectroscopy
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Colloquium: Quantum anomalous Hall effect
• One-dimensional Topological Edge States of Bismuth Bilayers
• Inverse Spin-Galvanic Effect in a Topological-Insulator/Ferromagnet Interface
• Surface quantized anomalous Hall current and magneto-electric effect in magnetically disordered topological insulators
• Crossover between weak localization and weak antilocalization in magnetically doped topological insulator
• Quintuple-layer epitaxy of high-quality Bi2Se3 thin films for topological insulator
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• Gapless surface Dirac cone in antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes
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• Imaging Dirac-Mass Disorder from Magnetic Dopant-Atoms in the Ferromagnetic Topological Insulator Cr${}_x$(Bi${}_{0.1}$Sb${}_{0.9}$)${}_{2-x}$Te${}_3$
• Electrically controllable surface magnetism on the surface of topological insulator
• Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects
• Weyl superconductors
• Impurity-induced states on the surface of 3D topological insulators
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• Magnetic Proximity Effect as a Pathway to Spintronic Applications of Topological Insulators
• Ordering of magnetic impurities and tunable electronic properties of topological insulators
• Photoemission Spectroscopy of Magnetic and Non-magnetic Impurities on the Surface of the Bi${}_2$Se${}_3$ Topological Insulator
• Tolerance of topological surface states towards magnetic moments: Fe on Bi2Te3 and Bi2Se3
• Fermi Level Tuning of Epitaxial Sb2Te3 Thin Films on Graphene by Regulating Intrinsic Defects and Substrate Transfer Doping
• Tailoring Exchange Couplings in Magnetic Topological Insulator/Antiferromagnet Heterostructures
• Magnetic proximity effect at the 3D topological insulator/magnetic insulator interface
• Tailoring Magnetic Doping in the Topological Insulator Bi2Se3
• Measurement of an Exceptionally Weak Electron-Phonon Coupling on the Surface of the Topological Insulator Bi${}_2$Se${}_3$ Using Angle-Resolved Photoemission Spectroscopy
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• Dynamics of magnetization on the topological surface
• Massive Dirac surface states in topological insulator/magnetic insulator heterostructures
• Stability, Electronic and Magnetic properties of magnetically doped topological insulators Bi2Se3, Bi2Te3 and Sb2Te3
• Long Range Intrinsic Ferromagnetism in Two Dimensional Materials and Dissipationless Future Technologies
• Electric charging of magnetic textures on the surface of a topological insulator
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• Dimensional Crossover Induced Topological Hall Effect in a Magnetic Topological Insulator
• Magnetic Doping and Kondo Effect in Bi2Se3 Nanoribbons
• Chemical potential dependent gap-opening at the Dirac surface states of Bi2Se3 induced by aggregated substitutional Cr atoms
• Quasiparticle scattering in two dimensional helical liquid
• Controllable magnetic doping of the surface state of a topological insulator
• Quantum anomalous Hall effect in magnetic topological insulators
• Surface magnetic ordering in topological insulators with bulk magnetic dopants
• One-dimensional edge state transport in a topological Kondo insulator
• Discovery of Weyl nodal lines in a single-layer ferromagnet
• RKKY interaction on the surface of three-dimensional Dirac semimetals
• Localized spin-orbit polaron in magnetic Weyl semimetal Co${}_3$Sn${}_2$S${}_2$
• Signatures of Dirac fermion-mediated magnetic order
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Electrically Tunable Magnetism in Magnetic Topological Insulators
• Theory of quasiparticle interference on the surface of a strong topological insulator
• Dual nature of magnetic dopants and competing trends in topological insulators
• Magnetic anisotropy effects on quantum impurities in superconducting host
• Current induced magnetization reversal on the surface of a topological insulator
• Magnetic-proximity-induced magnetoresistance on topological insulators
• Ferromagnetism and Spin-dependent Transport in n-type Mn-Bi2Te3 Thin Films
• Quantum anomalous vortex and Majorana zero mode in iron-based superconductor Fe(Te,Se)
• Magnetotransport and induced superconductivity in Bi based three-dimensional topological insulators
• Theoretical prediction of topological insulator in ternary rare earth chalcogenides
• Magnetoelectric Response of the Time-Reversal Invariant Helical Metal
• Systematics of electronic and magnetic properties in the transition metal doped Sb${}_2$Te${}_3$ quantum anomalous Hall platform
• Electrically tuned magnetic order and magnetoresistance in a topological insulator
• Helical edge states coupled to a spin bath: Current-induced magnetization
• Quantum impurity on the surface of a topological insulator
• Filling of magnetic-impurity-induced gap in topological insulators by potential scattering
• Electron-hole pairing in topological insulator thin film
• RKKY Interaction On Surfaces of Topological Insulators With Superconducting Proximity Effect
• Dynamical Axion Field in a Magnetic Topological Insulator Superlattice
• Interface-Induced Superconductivity in Magnetic Topological Insulator-Iron Chalcogenide Heterostructures
• Self-consistent theory of ferromagnetism on the surface of a topological insulator
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• Topological phase and edge states dependence of the RKKY interaction in zigzag silicene nanoribbon
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• Thermoelectric performance of classical topological insulator nanowires
• Kondo effect on the surface of 3D topological insulators: Signatures in scanning tunneling spectroscopy
• Quantum Anomalous Hall Effect in Magnetic Doped Topological Insulators and Ferromagnetic Spin-Gapless Semiconductors -- A Perspective Review
• Topological insulators in the quaternary chalcogenide compounds and ternary famatinite compounds
• Transverse magnetic heat transport on the topological surface
• Topological insulator Bi2Se3 thin films as an alternative channel material in MOSFETs
• Stationary phase approximation approach to the quasiparticle interference on the surface of a strong topological insulator
• Stabilization of Quantum Spin Hall Effect by Designed Removal of Time-Reversal Symmetry of Edge States
• Josephson and proximity effects on the surface of a topological insulator
• Anderson Impurity in Helical Metal
• Hysteretic Magnetotransport in SmB6 at Low Magnetic Fields
• Magnetotransport Measurements of the Surface States of Samarium Hexaboride using Corbino Structures
• Topological Crystalline Insulator Nanostructures
• Effect of Rashba splitting on RKKY interaction in topological insulator thin films
• Magnetic and defect probes of the SmB${}_6$ surface state
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• Mapping the Dirac fermions in intrinsic antiferromagnetic topological insulators (MnBi${}_2$Te${}_4$)(Bi${}_2$Te${}_3$)${}_n$ (n=0, 1)
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• Probing the wavefunction of the surface states in Bi${}_2$Se${}_3$ topological insulator: a realistic tight-binding approach
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• The topological surface state of $\alpha$-Sn on InSb(001) as studied by photoemission
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• Spin Helix of Magnetic Impurities in Two-dimensional Helical Metal
• Evidence for exchange Dirac gap in magneto-transport of topological insulator-magnetic insulator heterostructures
• Topological phase transitions driven by magnetic phase transitions in FexBi2Te3 (0 < x < 0.1) single crystals
• Indirect exchange interaction between magnetic impurities near the helical edge
• Many-body effects on superconductivity mediated by double-magnon processes in altermagnets
• Spin Susceptibility and Helical Magnetic Orders at the Edges/Surfaces of Topological Insulators Due to Fermi Surface Nesting
• Spin dynamics and magnetic interactions of Mn dopants in the topological insulator Bi${}_2$Te${}_3$
• Breaking time reversal symmetry in topological insulators
• Kondo Impurities Coupled to Helical Luttinger Liquid: RKKY-Kondo Physics Revisited
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• Electromagnetic spin polarization on the surface of topological insulator
• Large Itinerant Electron Exchange Coupling in the Magnetic Topological Insulator MnBi2Te4
• Multiband s-wave topological superconductors: role of dimensionality and magnetic field response
• Spin Orbit Torque in two dimensional Antiferromagnetic Topological Insulators
• Engineering the breaking of time-reversal symmetry in gate-tunable hybrid ferromagnet/topological insulator heterostructures
• Fractionalization and topology in amorphous electronic solids
• Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder
• Magnetic quantum phase transition in Cr-doped Bi2(SexTe1-x)3 driven by the Stark effect
• Noncollinear twisted RKKY interaction on the optically driven SnTe(001) surface
• Interaction driven surface Chern insulator in nodal line semimetals
• Exact edge, bulk and bound states of finite topological systems
• Spin textures and spin-wave excitations in doped Dirac-Weyl semimetals
• Topological orders competing for the Dirac surface state in FeSeTe surfaces
• Mass acquisition of Dirac fermions in Cr-doped topological insulator Sb2Te3 films
• Nontrivial interplay of strong disorder and interactions in quantum spin-Hall insulators doped with dilute magnetic impurities
• Unusual Dirac fermions on the surface of noncentrosymmetric $\alpha$ - BiPd superconductor
• Anisotropic RKKY interaction in spin polarized graphene
• Strong single-ion anisotropy and anisotropic interactions of magnetic adatoms induced by topological surface states
• On the interplay of paramagnetism and topology in the Fe-based High Tc Superconductors
• Topological Insulator Thin Films Starting from the Amorphous Phase - Bi${}_2$Se${}_3$ as Example
• Electronic properties of Bi${}_2$Se${}_3$ dopped by $3d$ transition metal (Mn, Fe, Co, or Ni) ions
• Impurity scattering on the surface of topological insulator thin films
• Gate-controlled one-dimensional channel on the topological surface
• Electron-magnon coupling and quasiparticle lifetimes on the surface of a topological insulator
• Visualizing the atomic-scale origin of metallic behavior in Kondo insulators
• Observation of backscattering induced by magnetism in a topological edge state
• Colossal anisotropy in diluted magnetic topological insulators
• Magnetic scattering of Dirac fermions in topological insulators and graphene
• Various magnetism of the compressed antiferromagnetic topological insulator EuSn2As2
• Ferromagnetic Anomalous Hall Effect in Cr-doped Bi${}_2$Se${}_3$ Thin Films via Surface-State Engineering
• Persistent Coherence and Spin-Polarization of Topological Surface States on Topological Insulators
• Focusing RKKY interaction by graphene P-N junction
• Synchrotron radiation induced magnetization in magnetically-doped and pristine topological insulators
• Functional Approach to Electrodynamics of Media
• Gap Generation in Topological Insulator Surface States by non-Ferromagnetic Magnets
• Co atoms on Bi${}_2$Se${}_3$ revealing a coverage dependent spin reorientation transition
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• Carrier dependent ferromagnetism in chromium doped topological insulator $C{r}_{0.2}B{i}_{x}S{b}_{1.8-x}T{e}_3$
• Observation of nonlinear planar Hall effect in magnetic insulator/topological insulator heterostructures
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• Gapless Topological Superconductors - Model Hamiltonian and Realization
• Andreev reflection in two-dimensional topological insulators with either conserved or broken time-reversal symmetry
• Velocity-determined anisotropic behaviors of RKKY interaction in 8-\textit{Pmmn} borophene
• Distinct Effects of Cr Bulk Doping and Surface Deposition on the Chemical Environment and Electronic Structure of the Topological Insulator Bi2Se3
• Indirect exchange interaction between magnetic impurities in the two-dimensional topological insulator based on CdTe/HgTe/CdTe quantum wells
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• Dirac-Fermion-Assisted Interfacial Superconductivity in Epitaxial Topological Insulator/Iron Chalcogenide Heterostructures
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• Effects of Defects and Dephasing on Charge and Spin Currents in Two-Dimensional Topological Insulators
• Surface Magnetism in Topological Crystalline Insulators
• Hinge Spin Polarization in Magnetic Topological Insulators Revealed by Resistance Switch
• Magnetic skyrmion crystal at a topological insulator surface
• Spin fluctuations in quantized transport of magnetic topological insulators
• Topologically Invariant Double Dirac States in Bismuth based Perovskites: Consequence of Ambivalent Charge States and Covalent Bonding
• Quantum impurity in the bulk of topological insulator
• Spontaneous gap generation on the surface of weakly interacting topological insulators using nonmagnetic impurities
• Photoinduced Quantum Anomalous Hall States in the Topological Anderson Insulator
• Magnetoelectric effect in topological insulator films beyond the linear response regime
• Controlling the Flow of Spin and Charge in Nanoscopic Topological Insulators
• Signature of Parity Anomaly: Crossover from One Half to Integer Quantized Hall Conductance in a Finite Magnetic Field
• Mesoscopic electron focusing in topological insulators
• Gate-defined coupled quantum dots in topological insulators
• Twisted magnetic topological insulators
• Magnetism-induced massive Dirac spectra and topological defects in the surface state of Cr-doped Bi${}_2$Se${}_3$-bilayer topological insulators
• Simultaneous Magnetic and Charge Doping of Topological Insulators with Carbon
• Aharonov-Bohm oscillations in the local density of topological surface states
• Two-dimensional ferromagnetic extension of a topological insulator
• Topological insulators in random potentials
• Topological magnon-photon interaction for cavity magnonics
• Direct observation of quantum anomalous vortex in Fe(Se,Te)
• Topological insulator ring with magnetic impurities
• Anomalous nuclear magnetic resonance spectra in Bi${}_2$Se${}_3$ nanowires
• Long-range interaction of magnetic moments in a coupled system of S/F/S Josephson junctions with anomalous ground-state phase shift
• Geometrically induced electric polarization in conical topological insulators
• Temperature Induced Spin Density Wave in Magnetic Doped Topological Insulators
• Soft-magnetic skyrmions induced by surface-state coupling in an intrinsic ferromagnetic topological insulator sandwich structure
• Gapless helical superconductivity on the surface of a three-dimensional topological insulator
• Enhanced Ferromagnetism in Monolayer Cr2Te3 via Topological Insulator Coupling
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• Spontaneous breaking of time-reversal symmetry at the edges of 1T' monolayer transition metal dichalcogenides
• Topological Phase Transitions Induced by Disorder in Magnetically Doped (Bi, Sb)${}_2$Te${}_3$ Thin Films
• Spin-spin interaction in the bulk of topological insulators
• Ferromagnetism and glassiness on the surface of topological insulators
• Electrical and thermoelectrical transport in Dirac fermions through a quantum dot
• Interplay between Mn-acceptor state and Dirac surface states in Mn-doped Bi${}_2$Se${}_3$ topological insulator
• Robustness of Gapless Interface State in a Junction of Two Topological Insulators
• Magnetic properties of Mn-doped Bi${}_2$Se${}_3$ topological insulators: ab initio calculations
• Massive Dirac Fermions and Strong Shubnikov-de Haas Oscillations in Topological Insulator Sm,Fe:Bi2Se3 Single Crystals
• Signature of parity anomaly in the measurement of optical Hall conductivity in quantum anomalous Hall systems
• Spin-selective tunneling from nanowires of the candidate topological Kondo insulator SmB6
• Two-Stage Proximity-Induced Gap-Opening in Topological Insulator - Insulating Ferromagnet (Bi${}_x$Sb${}_{1-x}$)${}_2$Te${}_3$ - EuS Bilayers
• Robust Gapless Surface State against Surface Magnetic Impurities on (Bi${}_{0.5}$Sb${}_{0.5}$)${}_2$Te${}_3$ Evidenced by In Situ Magnetotransport Measurements
• Anatomy of Spin and Current Generation from Magnetization Gradients in Topological Insulators and Rashba Metals
• Driving Topological Phases by Spatially Inhomogeneous Pairing Centers
• Magnetic impurities in an altermagnetic metal
• Magnetoconductance signatures of chiral domain-wall bound states in magnetic topological insulators
• Ab initio investigation of impurity-induced in-gap states in Bi${}_2$Te${}_3$ and Bi${}_2$Se${}_3$
• Classical spins in topological insulators
• Inelastic magnetic scattering effect on LDOS of topological insulators
• Residual gas absorption effect on the electronic structure of Cr-doped Bi2Se3
• Conductance oscillations in quantum point contacts of InAs/GaSb heterostructures
• Interplay of electronic structure and atomic ordering on surfaces: Momentum-resolved measurements of Cs atoms adsorbed on a Ag(111) substrate
• Dirac fermion wave guide networks on topological insulator surfaces
• Nature of the Dirac gap modulation and surface magnetic interaction in axion antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• High-performance nanoscale topological energy transduction
• Graphene with Rashba spin-orbit interaction and coupling to a magnetic layer: Electron states localized at the domain wall
• Disorder-induced phase transitions in double Weyl semimetals
• Single atom anisotropic magnetoresistance on a topological insulator surface
• RKKY coupling in Weyl semimetal thin films
• Exciton condensations in thin film topological insulator
• Effect of surface hybridization on RKKY coupling in ferromagnet/topological insulator/ferromagnet trilayer system
• Experimental demonstration of a magnetically induced warping transition in a topological insulator mediated by rare-earth surface dopants
• Floquet-driven indirect exchange interaction mediated by topological insulator surface states
• Non-local control of spin-spin correlation in finite geometry helical edge
• Surface Step Defect in 3D Topological Insulators: Electric Manipulation of Spin and Quantum Spin Hall Effect
• Resonant magneto-optic Kerr effect in the magnetic topological insulator Cr:(Sb${}_x$,Bi${}_{1-x}$)${}_2$Te${}_3$
• Topological matter: graphene and superfluid 3He
• Anomalous Spin Response and Virtual-Carrier-Mediated Magnetism in a Topological Insulator
• Anomalous Temperature Dependence of Quantum Correction to the Conductivity of Magnetic Topological Insulators
• Chiral Hall effect in the kink states in topological insulators with magnetic domain walls
• Spin Berry curvature of the Haldane model
• Unidirectional Seebeck effect in magnetic topological insulators
• Spin texture of an irradiated warped topological insulator surface
• Suppression of transport spin-polarization of surface states with emergence of ferromagnetism in Mn-doped Bi2Se3
• Quasiparticle states and quantum interference induce by magnetic impurities on a two-dimensional topological superconductor
• RKKY interaction in one-dimensional flat-band lattices
• Comparative Scanning Tunneling Microscopy Study on Hexaborides
• Hierarchy of relevant couplings in perturbative renormalization group transformations
• Anisotropic RKKY interactions mediated by $j=3/2$ quasiparticles in half-Heusler topological semimetal
• Influence of Helical Spin Structure on the Magnetoresistance of an Ideal Topological Insulator
• Topological insulator homojunctions including magnetic layers: the example of n-p type ($n$-QLs Bi${}_2$Se${}_3$/Mn-Bi${}_2$Se${}_3$) heterostructures
• Spatial anisotropy of Kondo screening cloud in a type-II Weyl semimetal
• $Z_2$ flux binding to higher-spin impurities in the Kitaev spin liquid
• Search for enhanced magnetism at the interface between Bi${}_2$Se${}_3$ and EuSe
• An STM perspective on hexaborides: Surface states of the Kondo insulator SmB${}_6$
• Local moment formation and magnetic coupling of Mn guest atoms in Bi${}_2$Se${}_3$: a low-temperature ferromagnetic resonance study
• Selective generation and amplification of RKKY interactions by P-N interface
• Electron transport in a ferromagnetic/normal/ferromagnetic tunnel junction based on the surface of a topological insulator
• Bound states and controllable currents on Topological Insulator surfaces with extended magnetic defects
• Spin Stiffness and Domain Walls in Dirac-Electron Mediated Magnets
• Proximity-induced nonlinear magnetoresistances on topological insulators
• Nested Defects on the Boundary of Topological Superconductors
• Nambu-Eliashberg theory for multi-scale quantum criticality : Application to ferromagnetic quantum criticality in the surface of three dimensional topological insulators
• Distinguishing Surface and Bulk Electromagnetism via Their Dynamics in an Intrinsic Magnetic Topological Insulator
• Three-dimensional symmetry breaking topological matters
• Optically and electrically controllable adatom spin-orbital dynamics in transition metal dichalcogenides
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• Topological insulator in a helicoidal magnetization field
• Diversified Ruderman-Kittel-Kasuya-Yosida Interactions in a Nonsymmorphic Crystal
• Dynamics of impurity in the environment of Dirac fermions
• Negative-U Superconductivity on the Surface of Topological Insulators
• RKKY interaction at helical edges of topological superconductors
• Theory of multiple magnetic scattering for quasiparticles on a gapless topological insulator surface
• Phonon and defect mediated quantum anomalous Hall insulator to metal transition in magnetically doped topological insulators
• Exchange and collective behavior of magnetic impurities in a disordered helical metal
• RKKY interaction in a spin-split superconductor
• Multiple scattering theory of quasiparticles on a topological insulator surface
• Bound-states and polarized charged zero modes in three-dimensional topological insulators induced by a magnetic vortex
• Formation of bound states from the edge states of 2D topological insulator by macroscopic magnetic barriers
• RKKY interaction in triplet superconductors: Dzyaloshinskii-Moriya-type interaction mediated by spin-polarized Cooper pairs
• RKKY interaction of magnetic impurities in node-line semimetals
• Structural, Surface Morphology and Magneto-Transport properties of Self Flux Grown Eu Doped Bi2Se3 Single Crystal
• Control of Plasmons in Topological Insulators via Local Perturbations
• Electron scattering by magnetic impurity in Weyl semimetals
• RKKY interaction in graphene at finite temperature
• Inter-surface interaction via phonon in three-dimensional topological insulator
• Doping-controlled surface conduction in topological insulators with warping effects
• Revealing Higher-Order Topological Bulk-boundary Correspondence in Bismuth Crystal with Spin-helical Hinge State Loop and Proximity Superconductivity
• First observation of spin-helical Dirac fermions and topological phases in undoped and doped Bi2Te3 demonstrated by spin-ARPES spectroscopy
• Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model
• Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals
• Magnetic torque oscillations from warped helical surface states in topological insulators
• The effect of midgap states on the magnetic exchange interaction mediated by a $d$-wave superconductor
• Quantum Transport and Magnetism of Dirac Electrons in Solids
• Transport theory for electrical detection of the spin texture and spin-momentum locking of topological surface states
• In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor
• Mössbauer parameters of ${}^{57}$Fe substituents in the topological insulator $B{i}_{2}S{e}_3$
• Charged magnons on the surface of a topological insulator
• RKKY interaction in helical higher-order topological insulators
• Unidirectional magneto-transport of linearly dispersing topological edge states
• Transmission of charge and spin in a topological-insulator-based magnetic structure
• Dzyaloshinskii-Moriya-type spin-spin interaction from mixed-parity superconductivity
• Enhancement of Curie Temperature in Ferromagnetic Insulator-Topological Insulator Heterostructures
• Localized magnetic moments in a Dirac semimetal as a spin model with long--range interactions
• Promoted current-induced spin polarization in inversion symmetry broken topological insulator thin films
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
• Strong photon coupling to high-frequency antiferromagnetic magnons via topological surface states
• Electron scattering in a superlattice of line defects on the surface of topological insulators
• Giant Spin Transport Anisotropy in Magnetic Topological Insulators
• Effects of iron doping on the topological insulator surfaces
• Surface chiral superconductivity in odd-parity nematic superconductors with magnetic impurities
• Surface states around a vortex in topological superconductors: Intersection of a surface and a vortex
• Gapped energy spectra around the Dirac node at the surface of a 3D topological insulator in the presence of the time-reversal symmetry
• Persistent ferromagnetism and topological phase transition at the interface of a superconductor and a topological insulator
• de Haas-van Alphen effect of correlated Dirac states in kagome metal Fe3Sn2
• Dirac Material Graphene
• Time-reversal invariant resonant backscattering on a topological insulator surface driven by a time-periodic gate voltage
• Current response of a topological insulator to a static Zeeman field
• Controllable magnetic correlation between two impurities by spin-orbit coupling in graphene
• Weak localization effect in topological insulator micro flakes grown on insulating ferrimagnet BaFe12O19
• Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points
• Self-consistent solution for the magnetic exchange interaction mediated by a superconductor
• Distinct topological excitonic insulators characterized by quantum geometry
• Bulk Saturable absorption in Topological Insulator thin Films