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Various nonlinear characteristics of solid states, such as the circular photogalvanic effect of time-reversal symmetric insulators, the quantized photogalvanic effect of Weyl semimetals, and the nonlinear Hall effect of time-reversal…
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 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…
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…
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…
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…
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…
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…
It is well known that a nontrivial Chern number results in quantized Hall conductance. What is less known is that, generically, the Hall response can be dramatically different from its quantized value in materials with broken inversion…
The valley Hall effect arises from valley contrasting Berry curvature and requires inversion symmetry breaking. Here, we propose a nonlinear mechanism to generate a valley Hall current in systems with both inversion and time-reversal…
The observation of non-linear Hall effects in time-reversal invariant systems has established the intriguing role of band topology beyond Berry curvature in determining transport phenomena. Many of these non-linear responses owe their…
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…
We study the quantum nonlinear Hall effect in two-dimensional materials with time-reversal symmetry. When only one mirror line exists, a transverse charge current occurs in second-order response to an external electric field, as a result of…
We investigate the nonlinear Hall responses in tunable two-dimensional Dirac materials. In particular, we study quantum geometry-driven second and third order non-linear responses in a time-reversal symmetric Dirac semimetal that can host…
Valley polarized twisted bilayer dice lattice hosts topologically nontrivial flat bands far from charge neutrality due to broken time reversal symmetry, whereas the ones in the vicinity of it remain topologically trivial. However, when both…
The nonlinear Hall effect due to Berry curvature dipole (BCD) induces frequency doubling, which was recently observed in time-reversal-invariant materials. Here we report novel electric frequency doubling in the absence of BCD on a surface…
In materials without inversion symmetry, Berry curvature dipole (BCD) arises from the uneven distribution of Berry curvature in momentum space. This leads to nonlinear anomalous Hall effects even in systems with preserved time-reversal…
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…
In recent years, it has been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall effect and the nonlinear Hall effect respectively. In this work, we demonstrate that Berry curvature multipoles (the…
Recent experiments have demonstrated interesting physics in a family of two-dimensional (2D) composition-tunable materials Nb$_{2n+1}$Si$_n$Te$_{4n+2}$. Here, we show that owing to its intrinsic low symmetry, metallic nature, tunable…