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The 'magnetoelectric effect' arises from the coupling between magnetic and electric properties in materials. The Z2 invariant of topological insulators (TIs) leads to a quantized version of this phenomenon, known as the topological…

Topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to…

Realizing axion insulator state with a uniform magnetization considerably facilitates experimental explorations of the intriguing topological magnetoelectric effect, a hallmark of three-dimensional (3D) topological insulators (TIs). Through…

Magnetic topological insulators (TIs) provide a highly tunable platform for engineering quantum states that emerge from the interplay between topology and magnetism. In this review article, we summarize experimental progress over the past…

A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI…

Constructing heterostructures of a topological insulator (TI) with an undoped magnetic insulator (MI) is a clean and versatile approach to break the time-reversible symmetry in the TI surface states. Despite a lot of efforts, the strength…

The electrodynamics of topological insulators (TIs) is described by modified Maxwell's equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such…

Magnetic topological states refer to a class of exotic phases in magnetic materials with their non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state,…

The intricate interplay between nontrivial topology and magnetism in two-dimensional (2D) materials has led to the emergence of many novel phenomena and functionalities. An outstanding example is the quantum anomalous Hall (QAH) effect,…

Engineering the anomalous Hall effect (AHE) in the emerging magnetic topological insulators (MTIs) has great potentials for quantum information processing and spintronics applications. In this letter, we synthesize the epitaxial Bi2Te3/MnTe…

A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport…

Three-dimensional topological insulators (TIs) are a perfectly tuned quantum-mechanical machinery in which counter-propagating and oppositely spin-polarized conduction channels balance each other on the surface of the material. This…

In a topological insulator (TI)/magnetic insulator (MI) hetero-structure, large spin-orbit coupling of the TI and inversion symmetry breaking at the interface could foster non-planar spin textures such as skyrmions at the interface. This is…

We demonstrate advantages of samples made by mechanical stacking of exfoliated van der Waals materials for controlling the topological surface state of a 3-dimensional topological insulator (TI) via interaction with an adjacent magnet…

We propose that the topological magneto-electric (ME) effect, a hallmark of topological insulators (TIs), can be realized in thin films of TIs in the $\nu=0$ quantum Hall state under magnetic field or by doping two magnetic ions with…

The quantum anomalous Hall effect (QAHE) that emerges under broken time-reversal symmetry in topological insulators (TI) exhibits many fascinating physical properties for potential applications in nano-electronics and spintronics. However,…

Three-dimensional topological insulators (TIs) have emerged as a unique state of quantum matter and generated enormous interests in condensed matter physics. The surfaces of a three dimensional (3D) TI are composed of a massless Dirac cone,…

Exotic quantum phenomena have been demonstrated in recently discovered intrinsic magnetic topological insulator MnBi2Te4. At its two-dimensional limit, quantum anomalous Hall (QAH) effect and axion insulator state are observed in odd and…

The search of novel topological phases, such as the quantum anomalous Hall insulator (QAHI) or the axion insulator, has motivated different schemes to introduce magnetism into topological insulators. One scheme is to introduce ferromagnetic…

Quantum anomalous Hall effect (QAHE), which generates dissipation-less edge current without external magnetic field, is observed in magnetic-ion doped topological insulators (TIs), such as Cr- and V-doped (Bi,Sb)2Te3. The QAHE emerges when…