Enhanced nonlinear Hall effect by Cooper pairs near superconductor criticality

TL;DR

This paper predicts a significant enhancement of the nonlinear Hall effect near superconducting criticality due to Cooper pair fluctuations, offering new insights into topological transport phenomena in superconductors.

Contribution

It introduces a theoretical framework showing how superconducting fluctuations amplify the nonlinear Hall response near criticality, linking Berry curvature dipole and Cooper pair dynamics.

Findings

Nonlinear Hall response is enhanced near superconducting criticality.

Superconducting fluctuations dominate the Hall response, not single electrons.

Potential for practical applications in topological electronics.

Abstract

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.