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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…
The recently discovered nonlinear Hall effect (NHE) in a few non-interacting systems provides a novel mechanism to generate second harmonic electrical Hall signals under time-reversal-symmetric conditions. Here, we introduce a new approach…
The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the…
The intrinsic magnetic layered topological insulator MnBi2Te4 with nontrivial topological properties and magnetic order has become a promising system for exploring exotic quantum phenomena such as quantum anomalous Hall effect. However, the…
Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom in addition to charge and spin. In the absence of inversion symmetry, these systems were predicted to exhibit opposite Hall effects for electrons…
This short review appears on the occasion of the fifth anniversary of discovery of intrinsic magnetic topological insulators (MTIs) of the MnBi${}_2$Te${}_4$ family, which have attracted a great deal of attention recently. This family of…
As the first intrinsic antiferromagnetic topological insulator, MnBi$_2$Te$_4$ has provided a platform to investigate the interplay of band topology and magnetism as well as the emergent phenomena arising from such an interplay. Here we…
Either in bulk form, or when exfoliated into atomically thin crystals, layered transition metal dichalcogenides are continuously leading to the discovery of new phenomena. The latest example is provided by 1T'-WTe$_2$, a semimetal recently…
We studied the nonlinear electric response in WTe2 and MoTe2 monolayers. When the inversion symmetry is breaking but the the time-reversal symmetry is preserved, a second-order Hall effect called the nonlinear anomalous Hall effect (NLAHE)…
The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K…
We report on low-temperature electron transport properties of MnSb2Te4, a candidate of ferrimagnetic Weyl semimetal. Long -range magnetic order is manifested as a nearly square-shaped hysteresis loop in the anomalous Hall resistance, as…
The nonlinear Hall effect, which is the second-order harmonic charge Hall effect from the Berry curvature dipole in momentum space, has received much attention recently. As the responses to higher harmonics of the driving ac electric field…
Introducing magnetism into topological insulators breaks time-reversal symmetry, and the magnetic exchange interaction can open a gap in the otherwise gapless topological surface states. This allows various novel topological quantum states…
Nonlinear transport phenomena in condensed matter reflect the geometric nature, quantum coherence, and many-body correlation of electronic states. Electric currents in solids are classified into (i) Ohmic current, (ii) supercurrent, and…
MnBi2Te4 has attracted tremendous research interest recently as the first intrinsic antiferromagnetic (AF) topological insulator. It undergoes a long-range AF order at TN = 24 K accompanied with a cusp-like anomaly in the metallic…
Exploring intrinsic magnetic topological insulators (TIs) for next-generation spintronic devices is still challenging in recent years. Here, we present a theoretical investigation on the electronic, magnetic and topological properties of…
Spintronics, an evolving interdisciplinary field at the intersection of magnetism and electronics, explores innovative applications of electron charge and spin properties for advanced electronic devices. The topological Hall effect, a key…
Bi2Se3 is an important semiconductor thermoelectric material and a prototype topological insulator. Here we report observation of Shubnikov-de Hass (SdH) oscillations accompanied by quantized Hall resistances (Rxy) in highly-doped n-type…
We study experimentally the transport properties of "inverted" semiconductor HgTe-based quantum well, which is related to the two-dimensional topological insulator, in diffusive transport regime. We perform nonlocal electrical measurements…
We propose an intrinsic nonlinear spin Hall effect, which enables the generation of collinearly-polarized spin current in a large class of nonmagnetic materials with the corresponding linear response being symmetry-forbidden. This opens a…