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Stacked two dimensional electron systems in transverse magnetic fields exhibit three dimensional fractional quantum Hall phases. We analyze the simplest such phases and find novel bulk properties, e.g., irrational braiding. These phases…
We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized…
This review presents recent breakthroughs in the realm of nonlinear Hall effects, emphasizing central theoretical foundations and recent experimental progress. We elucidate the quantum origin of the second-order Hall response, focusing on…
Two-dimensional systems with honeycomb lattice are known to be a paradigmatic platform to explore the various types of Hall effects, owing to that the interplay of lattice geometry, spin-orbit coupling and magnetism can give rise to very…
We report on the fate of the quantum Hall effect in graphene under strong laser illumination. By using Floquet theory combined with both a low energy description and full tight-binding models, we clarify the selection rules, the quasienergy…
Double-layer quantum Hall systems at total filling factor $\nu_T=1$ can exhibit a commensurate-incommensurate phase transition driven by a magnetic field $B_{\parallel}$ oriented parallel to the layers. Within the commensurate phase, the…
Valley-related multiple Hall effect and piezoelectric response are novel transport characteristics in low-dimensional system, however few studies have reported their coexistence in a single system as well as their coupling relationships. By…
We explore the emergence of spin-polarised flat-bands at head-to-head domain walls in a recently predicted class of antiferromagnetic topological insulators hosting planar magnetisation. We show, in the framework of quantum well physics,…
Carrier density and disorder are two crucial parameters that control the properties of correlated two-dimensional electron systems. In order to disentangle their individual contributions to quantum phenomena, independent tuning of these two…
We conduct experimental studies on the electrical transport properties of monolayer graphene directly covered by a few layers of $\rm CrI_3$. We do not observe the expected magnetic exchange coupling in the graphene but instead discover…
We have introduced a controllable nano-scale incursion into a potential barrier imposed across a two-dimensional electron gas, and report on the phenomena that we observe as the incursion develops. In the quantum Hall regime, the…
In this paper we theoretically predict a distinct class of anomalous Hall effects occurring in metallic collinear antiferromagnets. The effect is quadratic and $d-$wave symmetric in external magnetic field. In addition, the electric…
When monolayers of two-dimensional (2D) materials are stacked into van der Waals structures, interlayer electronic coupling can introduce entirely new properties, as exemplified by recent discoveries of moir\'e bands that host highly…
The topological phases of matter are characterized using the Berry phase, a geometrical phase, associated with the energy-momentum band structure. The quantization of the Berry phase, and the associated wavefunction polarization, manifest…
Valleytronic materials, characterized by local extrema (valley) in their bands, and topological insulators have separately attracted great interest recently. However, the interplay between valleytronic and topological properties in one…
Nonlinear charge transport, such as nonreciprocal longitudinal resistance and nonlinear Hall effect, has attracted considerable interest in probing the symmetries and topological properties of new materials. Recent research has revealed…
The chiral Luttinger liquid theory for fractional quantum Hall edge transport predicts universal power-law behavior in the current-voltage ($I$-$V$) characteristics for electrons tunneling into the edge. However, it has not been…
Two-dimensional materials are a fertile ground for exploring quantum geometric phenomena, with Berry curvature and its first moment, the Berry curvature dipole, playing a central role in their electronic response. These geometric properties…
Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment.…
We investigate the second-order anomalous Hall response in two-dimensional higher-wave symmetric magnets, including the recently discovered class of collinear magnets known as altermagnets, when subjected to a symmetry-breaking external…