Rectification and nonlinear Hall effect by fluctuating finite-momentum Cooper pairs

Nonreciprocal charge transport is attracting much attention as a novel probe and functionality of noncentrosymmetric superconductors. In this work we show that both the longitudinal and the transverse nonlinear paraconductivity are hugely enhanced in helical superconductors under moderate and high magnetic fields, which can be observed by second-harmonic resistance measurements. The discussion is based on the generalized formulation of nonlinear paraconductivity in combination with the microscopically determined Ginzburg-Landau coefficients. The enhanced nonreciprocal transport would be observable even with the cyclotron motion of fluctuating Cooper pairs, which is elucidated with a Kubo-type formula of the nonlinear paraconductivity. Nonreciprocal charge transport in the fluctuation regime is thereby established as a promising probe of helical superconductivity regardless of the sample dimensionality. Implications for the other finite-momentum superconducting states are briefly discussed.