Colloquium: Quantum anomalous Hall effect

Abstract

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken time-reversal symmetry. In Chern insulators, non-trivial bulk band topology is expressed by chiral states that carry current along sample edges without dissipation. The quantum anomalous Hall (QAH) effect refers to QH effects that occur in the absence of external magnetic fields due to spontaneously broken time-reversal symmetry. The QAH effect has now been realized in four different classes of two-dimensional materials: (i) thin films of magnetically (Cr- and/or V-) doped topological insulators in the (Bi,Sb)2Te3 family, (ii) thin films of the intrinsic magnetic topological insulator MnBi2Te4, (iii) moiré materials formed from graphene, and (iv ) moiré materials formed from transition metal dichalcogenides. In this Article, we review the physical mechanisms responsible for each class of QAH insulator, highlighting both differences and commonalities, and comment on potential applications of the QAH effect.

39 pages, 18 figures, comments are welcome

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• Direct evidence of ferromagnetism in MnSb2Te4
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• Perspective: 3D quantum Hall effect
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Cited by in corpus (173)

• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Large Quantum Anomalous Hall Effect in Spin-Orbit Proximitized Rhombohedral Graphene
• Quantum Anomalous Hall Effect in Antiferromagnetism
• Tunable moiré materials for probing Berry physics and topology
• Monolayer V2MX4: A new family of quantum anomalous Hall insulators
• Interface-Induced Superconductivity in Magnetic Topological Insulator-Iron Chalcogenide Heterostructures
• Tunable band topology and optical conductivity in altermagnets
• Non-linear Hall Effects: Mechanisms and Materials
• Confinement-Induced Chiral Edge Channel Interaction in Quantum Anomalous Hall Insulators
• Sublattice structure and topology in spontaneously crystallized electronic states
• Progress and prospects in the quantum anomalous Hall effect
• Intrinsic spin Hall torque in a moire Chern magnet
• Creation of Chiral Interface Channels for Quantized Transport in Magnetic Topological Insulator Multilayer Heterostructures
• Topological electronic crystals in twisted bilayer-trilayer graphene
• Experimental observation of exceptional bound states in a classical circuit network
• Generation of higher-order topological insulators using periodic driving
• Chern Number Tunable Quantum Anomalous Hall Effect in Compensated Antiferromagnets
• Electrically Controlled Anomalous Hall Effect and Orbital Magnetization in Topological Magnet MnBi2Te4
• Electrical Switching of the Edge Current Chirality in Quantum Anomalous Hall Insulators
• Engineering second-order topological insulators via coupling two first-order topological insulators
• Intrinsic magnetic topological insulators of the MnBi${}_2$Te${}_4$ family
• Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures
• Rules for dissipationless topotronics
• Fractional quantum anomalous Hall effect in a singular flat band
• Quantum Valley Hall effect without Berry curvature
• Intrinsic and tunable quantum anomalous Hall effect and magnetic topological phases in XYBi2Te5
• Ubiquitous order-disorder transition in the Mn antisite sublattice of the (MnBi${}_2$Te${}_4$)(Bi${}_2$Te${}_3$)${}_n$ magnetic topological insulators
• Engineering the in-plane anomalous Hall effect in Cd${}_3$As${}_2$ thin films
• Quantum anomalous Hall insulator in ionic Rashba lattice of correlated electrons
• Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices
• Coexistence of Superconductivity and Antiferromagnetism in Topological Magnet MnBi2Te4 Films
• Emergent Energy Dissipation in Quantum Limit
• Large-Gap Quantum Anomalous Hall Insulators in $A$Ti$X$ Class
• Feature-energy duality of topological boundary states in multilayer quantum spin Hall insulator
• High temperature, gate-free quantum anomalous Hall effect with an active capping layer
• Chiral-Flux-Phase-Based Topological Superconductivity in Kagome Systems with Mixed Edge Chiralities
• Signature of Parity Anomaly: Crossover from One Half to Integer Quantized Hall Conductance in a Finite Magnetic Field
• Interplay of Altermagnetic Order and Wilson Mass in the Dirac Equation: Helical Edge States without Time-Reversal Symmetry
• Interlayer Coupling Induced Topological Phase Transition to Higher Order
• Quantized Hall drift in a frequency-encoded photonic Chern insulator
• The Layer Hall Effect without External Electric Field
• Quantum Anomalous Hall Effect in Ferromagnetic Metals
• Emergent Haldane Model and Photon-Valley Locking in Chiral Cavities
• Berry Curvature Dipole and its Strain Engineering in Layered Phosphorene
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Evolution of Dopant-Concentration-Induced Magnetic Exchange Interaction in Topological Insulator Thin Films
• Two-dimensional Dirac fermions in a mass superlattice
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Atomic-Layer-Controlled Magnetic Orders in MnBi2Te4-Bi2Te3 Topological Heterostructures
• Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene
• Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets
• Engineering axion insulator phase in superlattices with inversion symmetry breaking
• Topological zero modes and correlation pumping in an engineered Kondo lattice
• Metallic Quantized Anomalous Hall Effect without Chiral Edge States
• Quantum computing topological invariants of two-dimensional quantum matter
• Orbital origin of fourfold anisotropic magnetoresistance in Dirac materials
• Atomic Scale Quantum Anomalous Hall Effect in Monolayer Graphene/$\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$ Heterostructure
• Observation of floating surface state in obstructed atomic insulator candidate NiP${}_2$
• Intrinsic Spin Nernst Effect and Chiral Edge Modes in van der Waals Ferromagnetic Insulators: Dzyaloshinskii-Moriya vs. Kitaev Interactions
• Topological $p_x+i{p}_y$ inter-valley coherent state in Moiré MoTe${}_2$/WSe${}_2$ heterobilayers
• Optical Switching of Moiré Chern Ferromagnet
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Evidence for Half-Quantized Chiral Edge Current in a C = 1/2 Parity Anomaly State
• Electrical control of intrinsic nonlinear Hall effect in antiferromagnetic topological insulator sandwiches
• Dissipation and dephasing in quantum Hall interferometers
• Antiferromagnetic Chern insulator with large charge gap in heavy transition-metal compounds
• Three-Dimensional Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness
• Symmetry-driven anisotropic coupling effect in antiferromagnetic topological insulator: Mechanism for high-Chern-number quantum anomalous Hall state
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• 5d orbital Induced Room Temperature Quantum Anomalous Hall Effect in TbCl
• Proximity-induced nonlinear magnetoresistances on topological insulators
• Non-Adiabatic Effect in Topological and Interacting Charge Pumping
• Intrinsic antiferromagnetic topological insulator and axion state in V2WS4
• Distinguishing Surface and Bulk Electromagnetism via Their Dynamics in an Intrinsic Magnetic Topological Insulator
• Topological magnons and domain walls in twisted bilayer MoTe${}_2$
• Néel Spin-Orbit Torque in Antiferromagnetic Quantum Spin and Anomalous Hall Insulators
• Thermal Hall conductivity of a valence bond solid phase in the square lattice $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction
• Observation of Temperature Independent Anomalous Hall Effect in Thin Bismuth from Near Absolute Zero to 300 K Temperature
• Engineering Plateau Phase Transition in Quantum Anomalous Hall Multilayers
• Edge supercurrent in Josephson junctions based on topological materials
• Chiral edge state coupling theory of transport in quantum anomalous Hall insulators
• CdTe and HgTe doped with V, Cr, and Mn -- prospects for the quantum anomalous Hall effect
• Tight-binding theory of spin-spin interactions, Curie temperatures, and quantum Hall effects in topological (Hg,Cr)Te in comparison to non-topological (Zn,Cr)Te, and (Ga,Mn)N
• Quantum Anomalous Hall Effect in $d$-Electron Kagome Systems: Chern Insulating States from Transverse Spin-Orbit Coupling
• Considerations for extracting moiré-level strain from dark field intensities in transmission electron microscopy
• Three-dimensional quantum anomalous Hall effect in Weyl semimetals
• Defect Engineering for Stabilizing Magnetic and Topological Properties in Mn(Bi1-xSbx)2Te4
• Nature of field-induced transitions and hysteretic magnetoresistance in non-collinear antiferromagnet EuIn2As2
• Spectroscopy and topological properties of a Haldane light system
• Experimentally Motivated Order of Length Scales Affect Shot Noise
• Interfacing Quantum Spin Hall and Quantum Anomalous Hall insulators: Bi bilayer on MnBi${}_2$Te${}_4$-family materials
• Environmental Doping-Induced Degradation of the Quantum Anomalous Hall Insulators
• Polariton Chern Bands in 2D Photonic Crystals Beyond Dirac Cones
• Half-Quantized Hall Metal and Marginal Metal in Disordered Magnetic Topological Insulators
• Density-Dependent Gauge Field with Raman Lattices
• Topologically-enhanced exciton transport
• Conductance asymmetry in proximitized magnetic topological insulator junctions with Majorana modes
• Magneto transport and first principle study of strong topological insulator gray Arsenic
• Anisotropic planar Hall effects in Bi${}_2$Se${}_3$/EuS interfaces: Deciphering the role of proximity induced spin canting and topological spin texture
• Chirality-tunable non-linear Hall effect
• Superlattice induced electron percolation within a single Landau level
• High-Chern-number Quantum anomalous Hall insulators in mixing-stacked MnBi${}_2$Te${}_4$ thin films
• Quantum theory of the magnetochiral anisotropy coefficient in ZrTe${}_5$
• Quantum Hall criticality in an amorphous Chern insulator
• Anomalous Fraunhofer-like patterns in quantum anomalous Hall Josephson junction
• Hermitian and non-Hermitian topology in active matter
• The electronic structure of intrinsic magnetic topological insulator MnBi2Te4 quantum wires
• Charge transport in chiral solids as a possible tool in search of dark matter signals
• Quantum-anomalous-Hall current patterns and interference in thin slabs of chiral topological superconductors
• Antiferromagnetic topological insulators in heavy-fermion systems
• Chiral excitonic systems in twisted bilayers from Förster coupling and unconventional excitonic Hall effects
• Chiral edge transport along domain walls in magnetic topological insulator nanoribbons
• Spectroscopic evidence of intra-unit-cell charge redistribution in charge-neutral magnetic topological insulator Sb-doped MnBi6Te10
• Quantum Geometric Origin of Orbital Magnetization
• Absence of Parity Anomaly in Massive Dirac Fermions on a Lattice
• Ferroelectric switching of quantum anomalous Hall effects in MnBi2Te4 films
• Interlayer Coupling-Induced Quantum Phase Transition in Quantum Anomalous Hall Multilayers
• Interface-Induced Stability of Nontrivial Topological Spin Textures: Unveiling Room-Temperature Hopfions and Skyrmions
• Identifying topological excitonic insulators via bulk-edge correspondence
• Spin texture tunability in Mn${}_{1-x}$Ge${}_x$Bi${}_2$Te${}_4$ through varying Ge Concentration
• Antiferromagnetic order in a layered magnetic topological insulator MnBi${}_2$Se${}_4$ probed by resonant soft x-ray scattering
• Designer spin-orbit superlattices: symmetry-protected Dirac cones and spin Berry curvature in two-dimensional van der Waals metamaterials
• In-plane magnetization orientation driven topological phase transition in OsCl${}_3$ monolayer
• Revisiting magnetic exchange interactions in transition metal doped Bi${}_2$Se${}_3$ using DFT+MFT
• Quantum Hall and Light Responses in a 2D Topological Semimetal
• Chiral edge plasmons in quantum anomalous Hall insulators
• Strong Field Optical Hall Effect in 2D Weyl Semimetal
• Relationship among Structural, Disordered, Magnetism and Band Topology in MnSb2Te4(Sb2Te3)n Family
• Orbital magnetization as the origin of the nonlinear Hall effect
• Tunable topological phase in 2D ScV${}_6$Sn${}_6$ kagome material
• Nucleation and Antiphase Twin Control in Bi${}_2$Se${}_3$ via Step-Terminated Al${}_2$O${}_3$ Substrates
• Mott transition and correlation effects on strictly localized states in an octagonal quasicrystal
• Substrate Effect on Electronic Band Structure and Topological Property in Monolayer V2O3 Magnetic Topological Insulator
• Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems
• Conductance oscillations of antiferromagnetic layer tunnel junctions
• Laser-induced topological phases in monolayer amorphous carbon
• Breakdown of the Wiedemann-Franz law in an interacting quantum Hall metamaterial
• Enhancement of Curie Temperature in Ferromagnetic Insulator-Topological Insulator Heterostructures
• Moire Engineering of Cooper-Pair Density Modulation States
• In-plane gate induced transition asymmetry of spin-resolved Landau levels in InAs-based quantum wells
• Chromium chalcohalide Janus monolayer ferromagnets with perpendicular magnetic anisotropy and high Curie temperature
• Quantum anomalous Hall effect with tunable Chern numbers induced by d-wave sublattice-staggered altermagnetism
• Floquet-Engineered Chern Insulator in two-dimensional $d_{x^2-y^2}$-Wave Altermagnets
• Proximity Magnetism in Mn(Bi,Sb)2Te4-(Bi,Sb)2Te3/MnTe Natural Heterostructures
• Extended Haldane Model in The Dice Lattice: Multiple Flat-Band-Induced topological Transitions Revealed
• Interface controlled Berry phase and anisotropic spin-charge conversion in altermagnet-topological insulator bilayers
• Topological spin-up triplet excitonic condensation in two-dimensional electron-hole systems
• Laughlin charge pumping from interplay of chiral Dirac and chiral Majorana modes
• Multi-tunneling effect of nonreciprocal Landau-Zener tunneling: Insights from DC field responses
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Disordered Parity Anomalous Semimetal
• Chiral Phonons Arising From Chirality-Selective Magnon-Phonon Coupling
• Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
• Interlayer Exchange Coupling-Induced Critical-Metal-to-Insulator Phase Transition in Quantum Anomalous Hall Insulators
• Magnetically tuned topological phase in graphene nanoribbon heterojunctions
• Elastic Constants and Bending Rigidities from Long-Wavelength Perturbation Expansions
• Anomalous Landau levels and quantum oscillation in rotation-invariant insulators
• Simple model for the gap in the surface states of the antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Relativistic Spin-Lattice Interaction Compatible with Discrete Translation Symmetry in Solids
• Direct observation of interfacial exchange coupling in a magnetic tunnel junction through spin-polarized quasiparticle interference
• High-Temperature Quantum Anomalous Hall Effect in Buckled Honeycomb Antiferromagnets
• Phaseless auxiliary-field quantum Monte Carlo method with spin-orbit coupling
• Quantum Christoffel Nonlinear Magnetization
• Spin adaptation of the cumulant expansions of reduced density matrices
• Many-body description of two-dimensional van der Waals ferroelectric $\alpha -$In${}_2$Se${}_3$
• Chern insulators in two and three dimensions: A global perspective
• Band engineering aided by topological edge state proximity effects: Inducing anti-chirality in graphene
• Designing Magnetic Topological Insulator Trilayers for Highly-Efficient Spin-Orbit Torque Switching
• Quantum anomalous Hall effect in chiral semimetals
• Sb doping effect on transport behavior in the topological insulator Bi2Se3