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In two-dimensional topological insulators, such as inverted HgTe/CdTe quantum wells, helical quantum spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field $B_\mathrm{c}$, above which only quantum Hall…

Topological surface-states can acquire an energy gap when time-reversal symmetry is broken by interfacing with a magnetic insulator. This gap has yet to be measured. Such topological-magnetic insulator heterostructures can host a quantized…

Quantum spin Hall insulators, recently realized in HgTe/(Hg,Cd)Te quantum wells, support topologically protected, linearly dispersing edge states with spin-momentum locking. A local magnetic exchange field can open a gap for the edge…

Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moir\'e materials provide a highly tunable platform for studies of electron correlation. Correlation-driven phenomena, including the…

The realization of long range and insulating ferromagnetic states in topological insulator (TI) has been a pressing issue since its discovery. Only recently, such state was achieved in Cr-doped Bi2-xSbxTe3, leading to the discovery of…

Recently, the intrinsic magnetic topological insulator MnBi2Te4 has attracted enormous research interest due to the great success in realizing exotic topological quantum states, such as the quantum anomalous Hall effect (QAHE), axion…

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in…

The algebra of observables of planar electrons subject to a constant background magnetic field B is given by A_theta(R^2) x A_theta(R^2) the product of two mutually commuting Moyal algebras. It describes the free Hamiltonian and the guiding…

Material defects remain as the main bottleneck to the progress of topological insulators (TIs). In particular, efforts to achieve thin TI samples with dominant surface transport have always led to increased defects and degraded mobilities,…

Planar Hall effect (PHE) in topological insulators (TIs) is discussed as an effect that stems mostly from conduction due to topologically protected surface states. Although surfaces states play a critical role and are of utmost importance…

We study the topological magnetoelectric effect on a conical topological insulator when a point charge $q$ is near the cone apex. The Hall current induced on the cone surface and the image charge configuration are determined. We also study…

The magnetic topological phases attract much interest, such as the axion insulator, higher-order topology, Weyl semimetals, and the quantum anomalous Hall effect (QAHE). Here, we predict that the axion insulator phase, magnetic Weyl points,…

Magnetically-doped topological insulators are intensely studied in the search for exotic phenomena such as the quantum anomalous Hall effect. The interplay of electronic and impurity degrees of freedom leads to the Kondo effect, an increase…

The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states through either sweeping the magnetic field or tuning the carrier density. The recent…

The quantum spin hall (QSH) phase, also known as the 2D topological insulator, is characterized by protected helical edge modes arising from time reversal symmetry. While initially proposed for band insulators, this phase can also manifest…

Quantum anomalous Hall effect (QAHE) has been experimentally observed in magnetically doped topological insulators. However, ultra-low temperature (usually below 300 mK), which is mainly attributed to inhomogeneous magnetic doping, becomes…

Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their…

MnBi$_2$Te$_4$ (MBT) is an ideal platform for studying the interplay between magnetism and topology. Many exotic topological phenomena, such as the quantum anomalous Hall effect and the axion insulator, have been observed in few-layer MBT.…

It is shown that the presence of matrix dipole moments induced by external electric fields can modify the Hall response in two dimensional Topological insulators. In the case of the Quantum Anomalous Hall effect the induced transverse…

We propose a memory device based on magnetically doped surfaces of 3D topological insulators. Magnetic information stored on the surface is read out via the quantized Hall effect, which is characterized by a topological invariant.…