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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,…
Fe$_{5-x}$GeTe$_2$ is a promising two-dimensional (2D) van der Waals (vdW) magnet for practical applications, given its magnetic properties. These include Curie temperatures above room temperature, and topological spin textures (TST or both…
In an intriguing recent experiment, it has been found that the two-dimensional (2D) surface states of a three-dimensional (3D) strong topological insulator (TI) support a non-zero Hall voltage transverse to an applied electric field even…
Recent work has extended topological band theory to open, non-Hermitian Hamiltonians, yet little is understood about how non-Hermiticity alters the topological quantization of associated observables. We address this problem by studying the…
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,…
We discover an intrinsic dipole Hall effect in a variety of magnetic insulating states at integer fillings of twisted MoTe$_2$ moir\'e superlattice, including topologically trivial and nontrivial ferro-, antiferro-, and ferri-magnetic…
We study theoretically the role of quenched magnetic disorder at the surface of a topological insulator by numerical simulation and scaling analysis. It is found that all the surface states are localized while the transverse conductivity is…
Topological insulators (TIs) in three space dimensions can be characterized by a quantized magnetoelectric coefficient. However, this coupling does not have experimentally observable consequences in the presence of time-reversal symmetry,…
The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity e2/h without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum…
The topological magnetoelectric effect (TME) is the fundamental quantization effect for topological insulators in units of the fine structure constant $\alpha$. In [Phys. Rev. Lett. 105, 166803(2010)], a topological quantization condition…
The search of new topological insulators that demonstrate the quantum anomalous Hall effect (QAHE) is a cutting-edge research topic in condensed matter physics and materials science. So far, the QAHE has been observed only in Cr-doped…
Quantum anomalous Hall effect (QAHE) has been experimentally realized in magnetically-doped topological insulators or intrinsic magnetic topological insulator MnBi$_2$Te$_4$ by applying an external magnetic field. However, either the low…
The quantized version of anomalous Hall effect realized in magnetic topological insulators (MTIs) has great potential for the development of topological quantum physics and low-power electronic/spintronic applications. To enable…
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,…
The quantum Hall effect is studied in the topological insulator BiSbTeSe$_2$. By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can…
Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral one-dimensional edge states. Yet, in magnetic topological insulators (MTI) to date, topological protection is far from robust,…
Motivated by the recent experimental realization of the half-quantized Hall effect phase in a three-dimensional (3D) semi-magnetic topological insulator [M. Mogi et al., Nature Physics 18, 390 (2022)], we propose a scheme for realizing the…
The quantum Hall effect (QHE) in two-dimensional (2D) electron gases, which is one of the most striking phenomena in condensed matter physics, involves the topologically protected dissipationless charge current flow along the edges of the…
The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quantum versions of the Hall effect and the spin…
The quantum anomalous Hall effect (QAHE) has been recently demonstrated in Cr- and V-doped three-dimensional topological insulators (TIs) at temperatures below 100 mK. In those materials, the spins of unfilled d-electrons in the transition…