Nonlinear hall effect in two-dimensional materials

Symmetry is a cornerstone of condensed matter physics, fundamentally shaping the behavior of electronic systems and inducing the emergence of novel phenomena. The Hall effect, a key concept in this field, demonstrates how symmetry breaking, particularly of time-reversal symmetry, influences electronic transport properties. Recently, the nonlinear Hall effect has extended this understanding by generating a transverse voltage that modulates at twice the frequency of the driving alternating current without breaking time-reversal symmetry. This effect is closely tied to the symmetry and quantum geometric properties of materials, offering a new approach to probing the Berry curvature and quantum metric. Here, we provide a review of the theoretical insights and experimental advancements in the nonlinear Hall effect, particularly focusing on its realization in two-dimensional materials. We discuss the challenges still ahead, look at potential applications for devices, and explore how these ideas might apply to other nonlinear transport phenomena. By elucidating these aspects, this review aims to advance the understanding of nonlinear transport effects and their broader implications for future technologies.