Hunting Majorana Fermions in Kitaev Magnets

Abstract

A Majorana fermion is a fermionic particle that is its own antiparticle. Since the theoretical discovery in 1937, the exotic particle has long been searched in particle physics. In the last few decades, however, it has attracted renewed interest in condensed matter physics, where it can be realized as an elementary excitation (quasiparticle) in quantum states of matter. In this review, we discuss another platform for Majorana fermions, the quantum spin liquid, in which interacting magnetic moments remain disordered down to the lowest temperature under strong quantum fluctuations. They are characterized by topological entanglement and fractional excitations, whose possible application to topological quantum computation is recently discussed intensively. As a prime candidate for such exotic states, we here focus on the Kitaev magnets, a subgroup of the spin-orbit Mott insulators. After a brief overview of the Kitaev model and the fractionalization of spins in the exact ground state, we review recent explosive development in this rapidly growing field, with a focus on numerical solutions of the Kitaev model at finite temperatures and the comparison with experiments. The key concept is thermal fractionalization --- two types of fractional excitations manifest themselves at largely different temperatures. This leads to distinct thermodynamics and spin dynamics in a variety of experimentally measurable quantities. We discuss such peculiar behaviors as the signatures of fractional quasiparticles, in careful comparison with the available experimental data for the candidate materials of the Kitaev magnets. Our review gives an overview of the current status of the identification of Majorana fermions in the Kitaev magnets, which would serve as a basis for further experimental and theoretical studies toward the manipulation of the exotic particles for topological quantum computation.

41 pages, 47 figures, accepted for publication in JPSJ as an invited review paper

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• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Raman Scattering Signatures of Kitaev Spin Liquids in A${}_2$ IrO${}_3$ Iridates
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Microscopic mechanism for higher-spin Kitaev model
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3
• Theory of the field-revealed Kitaev spin liquid
• Disorder in a quantum spin liquid: flux binding and local moment formation
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates $\beta$- and $\gamma$-Li${}_2$IrO${}_3$
• Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions : Approach From Bulk Calculations
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Spin-split band hybridization in graphene proximitized with $\alpha$-RuCl${}_3$ nanosheets
• Magnetic order in single crystals of Na3Co2SbO6 with a honeycomb arrangement of 3d${}^7$ Co${}^{2+}$ ions
• Electronic properties of α-RuCl3 in proximity to graphene
• Unconventional spin dynamics in the honeycomb-lattice material $\alpha$-RuCl${}_3$: high-field ESR studies
• Electronic Structure of the Kitaev Material $\alpha$-${\text{RuCl}}_3$ Probed by Photoemission and Inverse Photoemission Spectroscopies
• Kitaev materials beyond iridates: order by quantum disorder and Weyl magnons in rare-earth double perovskites
• Comprehensive study of the dynamics of a classical Kitaev spin liquid
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Impact of off-diagonal exchange interactions on the Kitaev spin liquid state of $\alpha$-RuCl${}_3$
• Confinement-Deconfinement Transition as an Indication of Spin-Liquid-Type Behavior in Na${}_2$IrO${}_3$
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Spin excitations of a proximate Kitaev quantum spin liquid realized in Cu${}_2$IrO${}_3$
• Crystalline Kitaev spin liquids
• Temperature evolution of spin dynamics in two- and three-dimensional Kitaev models: Influence of fluctuating gauge fluxes
• Topological superconductivity in the extended Kitaev-Heisenberg model
• Sudden quenching in the Kitaev honeycomb model: Study of defect and heat generation
• Coherent hole propagation in an exactly solvable gapless spin liquid

Cited by in corpus (182)

• Kitaev Spin Liquid in 3d Transition Metal Compounds
• Robustness of the thermal Hall effect close to half-quantization in a field-induced spin liquid state
• The Chemistry of Quantum Spin Liquids
• Spin-orbit-entangled electronic phases in 4$d$ and 5$d$ transition-metal compounds
• Sample dependence of the half-integer quantized thermal Hall effect in the Kitaev candidate $\alpha$-RuCl${}_3$
• Antiferromagnetic Kitaev interaction in $J_\rm{eff}=1/2$ cobalt honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Static and dynamic magnetic properties of honeycomb lattice antiferromagnets Na${}_2{M}_2$TeO${}_6$, $M$ = Co and Ni
• Excitations in the ordered and paramagnetic states of honeycomb magnet Na2Co2TeO6
• Theory of two-dimensional nonlinear spectroscopy for the Kitaev spin liquid
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Vacancy-induced low-energy density of states in the Kitaev spin liquid
• Phonon dynamics in the Kitaev spin liquid
• Thermodynamic and Transport Properties in Disordered Kitaev Models
• Electrical probes of the non-Abelian spin liquid in Kitaev materials
• Electrical Access to Ising Anyons in Kitaev Spin Liquids
• Dynamics of visons and thermal Hall effect in perturbed Kitaev models
• Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice
• Magnetism of Kitaev spin-liquid candidate material RuBr${}_3$
• Emergence of a nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets
• Magnetic Field Induced Spin Liquids in S=1 Kitaev Honeycomb Model
• Majorana-mediated spin transport without spin polarization in Kitaev quantum spin liquids
• Linear and Nonlinear Optical Responses in Kitaev Spin Liquids
• Towards Kitaev Spin Liquid in 3d Transition Metal Compounds
• Exploring Quantum Materials with Resonant Inelastic X-Ray Scattering
• Disorder upon disorder: localization effects in the Kitaev spin liquid
• Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
• Modified Curie-Weiss Law for $j_{\mathrm{eff}}$ Magnets
• Majorana-fermion origin of the planar thermal Hall effect in the Kitaev magnet $\alpha$-RuCl${}_3$
• Floquet engineering of Kitaev quantum magnets
• Computational design of $f$-electron Kitaev magnets: honeycomb and hyperhoneycomb compounds $A_2$PrO${}_3$ ($A=$ alkali metals)
• Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• Kitaev Quantum Spin Liquids
• Scanning tunneling spectroscopy of Majorana zero modes in a Kitaev spin liquid
• Presence and absence of itinerant gapless excitations in the quantum spin liquid candidate EtMe${}_3$Sb[Pd(dmit)${}_2$]${}_2$
• Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin structure factor, magnetic susceptibility, and NMR relaxation rate
• Universal Thermodynamics in the Kitaev Fractional Liquid
• Extraction of the interaction parameters for $\alpha -$RuCl${}_3$ from neutron data using machine learning
• Investigation of the magnetoelastic coupling anisotropy in the Kitaev material $\alpha$-RuCl${}_3$
• Kitaev magnetism through the prism of lithium iridate
• Possible Intermediate Quantum Spin Liquid Phase in $\alpha$-RuCl${}_3$ under High Magnetic Fields up to 100 T
• Evidence for the first-order topological phase transition in a Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Field-angle dependence of thermal Hall conductivity in magnetically ordered Kitaev-Heisenberg system
• Temperature evolution of the phonon dynamics in the Kitaev spin liquid
• Dynamics of a two-dimensional quantum spin-orbital liquid: spectroscopic signatures of fermionic magnons
• Probing signatures of fractionalization in candidate quantum spin liquid Cu2IrO3 via anomalous Raman scattering
• Further insights into the thermodynamics of the Kitaev honeycomb model
• Exchange interactions in $d^5$ Kitaev materials: From Na${}_2$IrO${}_3$ to $\alpha$-RuCl${}_3$
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
• Thermal spin dynamics of Kitaev magnets $-$ scattering continua and magnetic field induced phases within a stochastic semiclassical approach
• Electronic and magnetic properties of iridium ilmenites $A$IrO${}_3$ ($A=$ Mg, Zn, and Mn)
• Majorana correlations in the Kitaev model with ordered-flux structures
• Proximate Dirac spin liquid in honeycomb lattice $J_1$-$J_3$ XXZ model: Numerical study and application to cobaltates
• Magnon-spinon dichotomy in the Kitaev hyperhoneycomb $\beta$-Li${}_2$IrO${}_3$
• Dynamical anyon generation in Kitaev honeycomb non-Abelian spin liquids
• Analytic calculation of the vison gap in the Kitaev spin liquid
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Kitaev Spin Liquid Candidate OsxCl3 Comprised of Honeycomb Nano-Domains
• Flux mobility delocalization in the Kitaev spin ladder
• Flavor-wave theory with quasiparticle damping at finite temperatures: Application to chiral edge modes in the Kitaev model
• Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
• Phononic-magnetic dichotomy of the thermal Hall effect in the Kitaev-Heisenberg candidate material Na${}_2$Co${}_2$TeO${}_6$
• Quantized conductance with non-zero shot noise as a signature of Andreev edge state
• Defect-Induced Low-Energy Majorana Excitations in the Kitaev Magnet $\alpha$-RuCl${}_3$
• The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams
• Spin dynamics of the generalized quantum spin compass chain
• Field-induced phase transitions and quantum criticality in a honeycomb antiferromagnet Na3Co2SbO6
• Quasimolecular electronic structure of the spin-liquid candidate Ba${}_3$InIr${}_2$O${}_9$
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Update of $\mathcal{H}\Phi$: Newly added functions and methods in versions 2 and 3
• Electric-field control of magnetic anisotropies: applications to Kitaev spin liquids and topological spin textures
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• Magnetism in Kitaev Quantum Spin Liquid Candidate RuBr${}_3$
• SmI3: 4f5 honeycomb magnet with spin-orbital entangled Γ7 Kramers doublet
• Symmetry-protected gapless spin liquids on the strained honeycomb lattice
• Proximate Kitaev system for an intermediate magnetic phase in in-plane magnetic fields
• Introducing the monoclinic polymorph of the Kitaev magnet Na${}_2$Co${}_2$TeO${}_6$
• Tunable topological transitions in the frustrated magnet HoAgGe
• Epitaxial stabilization of (111)-oriented frustrated quantum pyrochlore thin films
• Two-step growth of high-quality single crystals of the Kitaev magnet $\alpha$-RuCl${}_3$
• Reentrant incommensurate order and anomalous magnetic torque in the Kitaev magnet $\beta$-${\text{Li}}_2{\text{IrO}}_3$
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$
• Feasibility of Kitaev quantum spin liquids in ultracold polar molecules
• RIXS interferometry and the role of disorder in the quantum magnet Ba${}_3$Ti${}_{3-x}$Ir${}_x$O${}_9$
• Scattering phenomena for spin transport in Kitaev spin liquid
• Thermodynamic evidence for field-angle dependent Majorana gap in a Kitaev spin liquid
• Phonon Dynamics in the Generalized Kitaev Spin Liquid
• Quantum paramagnetism in the hyperhoneycomb Kitaev magnet $\beta$-ZnIrO${}_3$
• Role of Majorana fermions in spin transport of anisotropic Kitaev model
• CaCo${}_2$TeO${}_6$: A topochemically prepared 3$d^7$ honeycomb Kitaev magnet
• Stabilization of a honeycomb lattice of IrO${}_6$ octahedra in superlattices with ilmenite-type MnTiO${}_3$
• Improved Honeycomb and Hyperhoneycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories
• Electronic excitations in $5d^4$ J=0 Os${}^{4+}$ halides studied by RIXS and optical spectroscopy
• Islands of Chiral Solitons in Integer Spin Kitaev Chains
• Spin- and Flux-gap Renormalization in the Random Kitaev Spin Ladder
• Magnetic-field Induced Topological Transitions and Thermal Conductivity in a Generalized Kitaev Model
• Magnon Condensation in Dimerized Antiferromagnets with Spin-Orbit Coupling
• Asymmetric modulation of Majorana excitation spectra and nonreciprocal thermal transport in the Kitaev spin liquid under a staggered magnetic field
• Field-Angle-Resolved Specific Heat in Na${}_2$Co${}_2$TeO${}_6$: Evidence against Kitaev Quantum Spin Liquid
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Majorana Fermion Mean-Field Theories of Kitaev Quantum Spin Liquids
• Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field
• Field-driven spatiotemporal manipulation of Majorana zero modes in a Kitaev spin liquid
• Molecular Orbital Electronic Instability in the van der Waals Kagome Semiconductor Nb${}_3$Cl${}_8$: Exploring Future Directions
• Stabilization of a Majorana Zero Mode through Quantum Frustration
• Raman Scattering Polarization and Single Spinon Identification in Two-Dimensional Kitaev Quantum Spin Liquids
• Dynamic Jahn-Teller Phenomena in Heavy Transition Metal Compounds
• Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids
• Dimer Crystallization Induced by Elemental Substitution in the Honeycomb Lattice of Ru1-xOsxCl3
• Exploring rare-earth Kitaev magnets by massive-scale computational analysis
• Interedge spin resonance in the Kitaev quantum spin liquid
• $J_{\mathrm{eff}}$ = 1/2 Hyperoctagon Lattice in Cobalt Oxalate Metal-Organic-Framework
• Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Polymorphism and Magnetism in a Kitaev Honeycomb Cobaltate KCoAsO${}_4$
• High-temperature magnetic anomaly via suppression of antisite disorder through synthesis route modification in a Kitaev candidate Cu${}_2$IrO${}_3$
• Non-local features of the spin-orbit exciton in Kitaev materials
• Projective-symmetry-group analysis of inelastic light scattering in Kitaev spin balls
• Local spin-flip transitions induced by magnetic quantum impurities in two-dimensional magnets
• Theory of quasiparticle interference in Kitaev quantum spin liquids
• Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids
• Static and fluctuating zigzag order, and possible signatures of Kitaev physics, in torque measurements of $\alpha$-RuCl${}_3$
• Sound attenuation in the hyperhoneycomb Kitaev spin liquid
• Field-Induced Ordered Phases in Anisotropic Spin-1/2 Kitaev Chains
• Intermediate phases in $\alpha$-RuCl${}_3$ under in-plane magnetic field via interlayer spin interactions
• Monoclinic distortion in hyperhoneycomb Kitaev material $\beta$-ZnIrO${}_3$ revealed by improved sample quality
• Finite-momentum energy dynamics in a Kitaev magnet
• Bulk excitations in ultraclean $\alpha$-RuCl${}_3$: Quantitative evidence for Majorana dispersions in a Kitaev quantum spin liquid
• Exchange Interactions in Rare-earth Magnets $A_2$PrO${}_3$ ($A$= alkali metals): Revisited
• Pairing tendencies in the doped Kitaev-Heisenberg model
• Possible Realization of Kitaev Spin Liquids in van der Waals Heterostructures of $\alpha$-RuCl${}_3$ and Cr$X_3$ ($X$=Cl and I)
• Assembling Kitaev honeycomb spin liquids from arrays of 1D symmetry protected topological phases
• Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation
• (H,Li)${}_6$Ru${}_2$O${}_6$ : a possible zero-field Ru${}^{3+}$-based Kitaev Quantum Spin Liquid
• Mixed-State Quantum Spin Liquids and Dynamical Anyon Condensations in Kitaev Lindbladians
• Coupled spin-1/2 antiferromagnetic chain Cs${}_2$LiRuCl${}_6$ with partially disordered crystal lattice
• Vacancies in generic Kitaev spin liquids
• Formulation of spin Nernst effect for spin-nonconserving insulating magnets
• Majorana Gap Formation in the Anisotropic Kitaev Model with Ordered Flux Configuration
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Field-direction Dependence of Majorana-mediated Spin Transport
• Electric polarization near vortices in the extended Kitaev model
• Robustness of Vacancy-Bound Non-Abelian Anyons in the Kitaev Model in a Magnetic Field
• Strain-induced Landau levels of Majorana fermions in an anisotropically interacting Kitaev model on a honeycomb lattice
• Topological Characterization of Kitaev Spin Nanoribbons with Ordered Flux Configurations
• Coupled-cluster approach to vibronic effects in resonant inelastic x-ray scattering of quantum materials: Application to a $5d^1$ rhenium oxide
• Static and Dynamical Spin Correlations in the Kitaev Model at Finite Temperatures via Green's Function Equation of Motion
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model
• Spin-Spin Correlations in the Kitaev Model at Finite Temperatures: Approximate and Exact Results via Green's Function Equation of Motion
• Magnetic ordering in the $J_{\mathrm{eff}}$ = 0 Nickelate NiRh${}_2$O${}_4$ prepared via a solid-state metathesis
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry
• Dynamical spin correlations in kagome antiferromagnets: comparison of Abrikosov fermion and Schwinger boson approaches beyond mean field
• Photoinduced Pseudospin Polarization in a Three-Orbital Hubbard Model
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• Coexistence of static and dynamic local magnetic fields in an S = 3/2 honeycomb lattice antiferromagnet Co2Te3O8
• Majorana Signatures in Planar Tunneling through a Kitaev Spin Liquid
• Vortex creation and control in the Kitaev spin liquid by local bond modulations
• Dominant Kitaev Interaction and Field-induced Quantum Disordered Phase in the Cobaltate Na${}_2$Co${}_2$TeO${}_6$
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers
• Non-Loudon-Fleury Raman scattering in spin-orbit coupled Mott insulators
• Realizing Majorana fermion modes in the Kitaev model
• Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to ${\mathrm{SmI}}_3$
• Tuning the Chern number of Kitaev quantum spin liquid
• The field-angle anisotropy of proximate Kitaev systems under an in-plane magnetic field
• Spin disorder state induced by Mg${}^{2+}$ doping in a Kitaev material Na${}_3$Co${}_2$SbO${}_6$
• Magnetic field effects on the Kitaev model coupled to environment
• Spin-liquid and spin-glass behavior in quantum spin models with all-to-all p-spin interactions
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
• Ground state of the staggered Heisenberg-$\Gamma$ honeycomb model in a magnetic field
• Metallic ruthenium ilmenites: first-principles study of MgRuO${}_3$ and CdRuO${}_3$
• Susceptibility anisotropy and absence of ferroelectric order in the Kitaev spin liquid candidate Na${}_2$Co${}_2$TeO${}_6$
• Flux-induced midgap states between strain-engineered flat bands