Ratchet Hall effect in fluctuating superconductors

We propose a superconducting ratchet-induced Hall effect (RHE), characterized by the emergence of a unidirectional, rectified flux of fluctuating Cooper pairs in a two-dimensional thin film exposed to an external electromagnetic field. The RHE is a second-order response with respect to the electromagnetic field amplitude. It consists of a nonzero photocurrent due to the breaking of the system's inversion symmetry driven by the combined action of the in-plane time-dependent electric field and a spatial modulation of the critical temperature. We explore a means to control the electric current by the polarization of the external field accompanied by a nonlinear Hall effect of fluctuating Cooper pairs caused by circularly polarized irradiation. Moreover, the nonlinear conductivity tensor exhibits a higher-power dependence on the reduced temperature compared to that of the conventional Aslamazov-Larkin correction (or other fluctuating second-order nonlinear responses). It results in a dramatic enhancement of the nonlinear Hall response of fluctuating Cooper pairs in the vicinity of the superconducting criticality.