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From the low-energy model, the topological field theory indicates that the surface magnetization can open a surface gap in 3D topological insulators (TIs), resulting in a half-quantized Hall conductance. Here by employing the realistic…
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…
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…
Three-dimensional topological insulators of finite thickness can show the quantum Hall effect (QHE) at the filling factor $\nu=0$ under an external magnetic field if there is a finite potential difference between the top and bottom…
The quantum spin Hall effect (QSHE), a hallmark of topological insulators, enables dissipationless, spin-polarized edge transport and has been predicted in various two-dimensional materials. However, challenges such as limited scalability,…
The quantum anomalous Hall effect (QAHE), characterized by dissipationless quantized edge transport, relies crucially on a non-trivial topology of the electronic bulk bandstructure and a robust ferromagnetic order that breaks time-reversal…
The discovery of topological states of matter has profoundly augmented our understanding of phase transitions in physical systems. Instead of local order parameters, topological phases are described by global topological invariants and are…
We report on the scaling behavior of V-doped (Bi,Sb)$_2$Te$_3$ samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a…
The quantum anomalous Hall effect in magnetic topological insulators has been recognized as a promising platform for applications in quantum metrology. The primary reason for this is the electronic conductance quantization at zero external…
Axion electrodynamics, first proposed in the context of particle physics, manifests itself in condensed matter physics in the topological field theory description of 3d topological insulators and gives rise to magnetoelectric effect, where…
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…
Realization of the quantum anomalous Hall effect and axion electrodynamics in topological materials are among the paradigmatic phenomena in condensed matter physics. Recently, signatures of both phases are observed to exist in thin films of…
Conventional topological Hall effects (THE) require conducting magnets, leaving insulating systems largely inaccessible. Here we introduce the interfacial topological Hall effect (ITHE), where the noncoplanar spin textures of insulating…
The magnetic topological insulator MnBi$_{6}$Te$_{10}$ has emerged as a promising candidate for realizing the quantum anomalous Hall effect (QAHE), owing to its ability to retain ferromagnetism through precise control of anti-site defects.…
The quantum anomalous Hall (QAH) state is a two-dimensional bulk insulator with a non-zero Chern number in absence of external magnetic fields. Protected gapless chiral edge states enable dissipationless current transport in electronic…
Intrinsic magnetic topological insulators offer low disorder and large magnetic bandgaps for robust magnetic topological phases operating at higher temperatures. By controlling the layer thickness, emergent phenomena such as the Quantum…
We use Dirac quantization of flux to study fractional charges and axion angles \theta in interacting topological insulators with gapless surface modes protected by time-reversal symmetry. In interacting topological insulators, there are two…
By breaking the time-reversal-symmetry in three-dimensional topological insulators with introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect…
Nonlinear Hall effect (NHE) can be generated via Berry curvature dipole (BCD) on nonequilibrium Fermi surface in a non-magnetic system without inversion symmetry.To achieve a large BCD, strong local Berry curvatures and their variation with…
The layer Hall effect is an intriguing phenomenon observed in magnetic topological layered materials, where the Hall response arises from the opposite deflection of electrons on top and bottom layers. To realize layer Hall effect,…