Quantum anomalous Hall effect in magnetic topological insulators

Abstract

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimension (2D) and three-dimension (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We present the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. We discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.

13 pages, 11 figures. Invited Review to Physica Scripta, Nobel Physica Symposium on New Forms of Matter: Topological Insulators and Superconductors

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Cited by in corpus (58)

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• Flat Chern Band From Twisted Bilayer MnBi${}_2$Te${}_4$
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• Monolayer V2MX4: A new family of quantum anomalous Hall insulators
• Multifunctional Two-dimensional van der Waals Janus Magnet Cr-based Dichalcogenide Halides
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• Intrinsic topological phases in Mn${}_2$Bi${}_2$Te${}_5$ tuned by the layer magnetization
• In-Plane Magnetization Induced Quantum Anomalous Hall Effect in Atomic Crystals of Group-V Elements
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Quantum anomalous Hall effect in two-dimensional magnetic insulator heterojunctions
• Floquet topological insulator phase in a Weyl semimetal thin film with disorder
• Effects of Domain Walls in Quantum Anomalous Hall Insulator/Superconductor Heterostructures
• Time-reversal symmetry breaking driven topological phase transition in EuB${}_6$
• In-Plane Magnetic-Field-Induced Quantum Anomalous Hall Plateau Transition
• Axion Insulator State in a Ferromagnet/Topological Insulator/Antiferromagnet Heterostructure
• Progress and prospects in the quantum anomalous Hall effect
• Topological quantum phase transition in magnetic topological insulator upon magnetization rotation
• Electrically tunable topological superconductivity and Majorana fermions in two dimensions
• Surface charge conductivity of topological insulator in a magnetic field: effect of hexagonal warping
• Axion Insulator State with ferromagnetic ordering in CrI3/Bi2Se3/MnBi2Se4 Heterostructure
• Chiral torsional effect with finite temperature, density and curvature
• Nearly triple nodal point topological phase in half-metallic GdN
• Quantum Anomalous Parity Hall Effect in Magnetically Disordered Topological Insulator Films
• Unusual Intralayer Ferromagnetism Between S = 5/2 ions in MnBi${}_2$Te${}_4$: Role of Empty Bi $p$ States
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• Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators
• Partial Charge Transfer and Absence of Induced Magnetization in EuS(111)/Bi${}_2$Se${}_3$ Heterostructures
• Hexagon Ising-Kondo lattice: An implication for intrinsic antiferromagnetic topological insulator
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• Low-energy modeling of three-dimensional topological insulator nanostructures
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• Distinguishing Surface and Bulk Electromagnetism via Their Dynamics in an Intrinsic Magnetic Topological Insulator
• Fermi level dependence of magnetism and magnetotransport in the magnetic topological insulators Bi${}_2$Te${}_3$ and BiSbTe${}_3$ containing self-organized MnBi${}_2$Te${}_4$ septuple layers
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• Planar magnetic texture on the surface of a topological insulator
• Born approximation study of the strong disorder in magnetized surface states of topological insulator
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• Spectroscopic evidence of intra-unit-cell charge redistribution in charge-neutral magnetic topological insulator Sb-doped MnBi6Te10
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• Quantum anomalous Hall conductivity in altermagnets under applied magnetic field
• Optimizing proximitized magnetic topological insulator nanoribbons for Majorana bound states
• Are thermal fluctuations the sole reason for finite longitudinal resistance in quantum anomalous Hall experiments?
• Synthesis of intrinsic magnetic topological insulator MnBi2nTe3n+1 family by chemical vapor transport method with feedback regulation