Nonlinear ac Hall effect in two-dimensional superconductors

We propose a nonlinear ac Hall effect in two-dimensional BCS single-band superconductors. Namely, a nonlinear ac transverse Hall current emerges in the superconductor interacting with an incident polarized light if a built-in dc supercurrent is present in the system. Applying the nonequilibrium Keldysh diagram technique, we calculate an ac Hall current density oscillating at double the electromagnetic field frequency. This current's strength is influenced by the inelastic relaxation rate, the dc supercurrent direction, and light polarization, with the ac current density being tunable via electron density. The ac Hall effect is unique to the superconducting state and is shaped by temperature, light frequency, and material characteristics.