The Hall effects comprise one of the oldest but most vital fields in condensed matter physics,
and they persistently inspire new findings, such as quantum Hall effects and topological …

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 …

This review presents recent breakthroughs in the realm of nonlinear Hall effects,
emphasizing central theoretical foundations and recent experimental progress. We elucidate …

Topological Weyl semimetals (WSMs) have been predicted to be excellent candidates for
detecting Berry curvature dipole (BCD) and the related nonlinear effects in electronics and …

The study of the nonlinear anomalous Hall effect (NLAHE) in PT-symmetric systems has
focused on intrinsic mechanisms. Here, we show that disorder contributes substantially to …

Time reversal and inversion symmetric materials fail to yield linear and nonlinear responses
since they possess net zero Berry curvature. However, higher-order Hall response can be …

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 …

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 …

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 …

Three-dimensional Hopf insulators are a class of topological phases beyond the tenfold-way
classification. At the critical point of the transition between two distinct Hopf insulators with …