Planar Hall effect from superconducting fluctuations

We investigate the planar Hall effect (PHE) in two-dimensional (2D) superconductors with spin-orbit interactions, where transport anisotropy is induced by an in-plane magnetic field. While PHE typically arises from the breaking of basal mirror symmetry, when the field exclusively couples to spin degrees of freedom, it remains negligible in noninteracting systems. In this study, we explore anisotropic paraconductivity as an alternative mechanism for PHE observed in 2D superconductors in the normal state. Due to the momentum dependence of spin-orbit interactions, the field-induced pair breaking exhibits anisotropy. To elucidate this phenomenon, we compute the PHE for the Rashba spin-orbit interaction. Our analysis reveals that Cooper pairs propagating along the field experience stronger pair breaking compared to those moving perpendicular to the field. This physical insight is corroborated by explicit calculations of paraconductivity.