Enhanced nonlinear Hall effect by Cooper pairs near superconductor criticality

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 symmetry. Interestingly, the presence of time-reversal symmetry is consistent with and thus allows a direct transition into a superconducting phase. Indeed, superconductivity has been established in various nonlinear Hall materials, such as WTe$_2$ and MoTe$_2$, at sufficiently low temperatures. We find that the nonlinear Hall response should be significantly enhanced near the superconducting criticality, dominated by the Aslamazov-Larkin (AL) contributions augmented by superconducting fluctuations, which we attribute to the Berry curvature dipole and a divergent lifetime $\tau\sim (T-T_c)^{-1}$ of the Cooper pairs, instead of the single electrons. Such a controlled enhancement brings the nonlinear Hall effect into various simple experimental observations and practical applicational potentials.