Enhanced nonlinear Hall effect by Cooper pairs near the superconducting phase transition

Unlike the linear Hall effect, which requires broken time-reversal symmetry, the nonlinear Hall effect may occur in time-reversal-symmetric systems as long as a nonzero Berry curvature dipole exists 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 ${\mathrm{WTe}}_{2}$ and ${\mathrm{MoTe}}_{2}$, at sufficiently low temperatures. We find that the nonlinear Hall response should be significantly enhanced near the superconducting criticality, dominated by the Aslamazov-Larkin contributions augmented by superconducting fluctuations, which we attribute to the Berry curvature dipole and a divergent lifetime $\ensuremath{\tau}\ensuremath{\sim}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}1}$ 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.