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The Hall effect occurs only in systems with broken time-reversal symmetry, such as solids under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE). Here we show a new Hall effect…
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…
It is well-known that a non-vanishing Hall conductivity requires time-reversal symmetry breaking. However, in this work, we demonstrate that a Hall-like transverse current can occur in second-order response to an external electric field in…
The anomalous Hall effect in time-reversal symmetry broken systems is underpinned by the concept of Berry curvature in band theory. However, recent experiments reveal that the nonlinear Hall effect can be observed in non-magnetic systems…
The ordinary Hall effect refers to generation of a transverse voltage upon exertion of an electric field in the presence of an out-of-plane magnetic field. While a linear Hall effect is commonly observed in systems with breaking…
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…
The appearance of a Hall conductance necessarily requires breaking of time-reversal symmetry, either by an external magnetic field or by the internal magnetization of a material. However, as a second response, Hall dissipationless…
In the presence of time reversal symmetry, a non-linear Hall effect can occur in systems without an inversion symmetry. One of the prominent candidates for detection of such Hall signals are Weyl semimetals. In this article, we investigate…
In topological materials, Berry curvature leads to intrinsic Hall responses. Focusing on time-reversal symmetric systems with broken inversion symmetry, a spontaneoous (zero magnetic field) Hall effect is expected to develop under an…
The non-linear generalization of the Hall effect has recently gained much attention, with a rapidly growing list of non-centrosymmetric materials that display higher-order Hall responses under time-reversal invariant conditions. The…
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 observation of a Hall effect, a finite transverse voltage induced by a longitudinal current, usually requires the breaking of time-reversal symmetry, for example through the application of an external magnetic field or the presence of…
Nonlinear anomalous Hall effect is the Berry curvature dipole induced second-order Hall voltage or temperature difference in response to a longitudinal electric field or temperature gradient. These are the prominent Hall responses in time…
It has recently been demonstrated that various topological states, including Dirac, Weyl, nodal-line, and triple-point semimetal phases, can emerge in antiferromagnetic (AFM) half-Heusler compounds. However, how to determine the AFM…
Unlike the linear Hall effect that requires broken time-reversal symmetry, the nonlinear Hall effect may occur in time-reversal symmetric systems as long as there exists a non-zero Berry curvature dipole in the absence of inversion…
We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed -- the Weyl cones are "tilted" -- the concerted actions of the anomalous velocity…
The anomalous Hall effect describes the generation of a transverse voltage by a longitudinal current even in the absence of an external magnetic field. While typically observed in ferromagnets, it has also been predicted to arise in…
The recent observations of nonlinear Hall effect in time-reversal symmetry protected systems and on the surface of three-dimensional topological insulators due to an in-plane magnetic field have attracted immense experimental and…
Time-reversal symmetry breaking is the basic physics concept underpinning many magnetic topological phenomena such as the anomalous Hall effect (AHE) and its quantized variant. The AHE has been primarily accompanied by a ferromagnetic…
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…