Ratchet Hall Effect in Fluctuating Superconductors

Abstract

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 non-linear 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 non-linear Hall response of fluctuating Cooper pairs in the vicinity of the superconducting criticality.

Figures (2)

• Figure 1: System schematic: (a) A superconducting thin film with modulated critical temperature in a normal state ($T\gtrsim T_c(x)$) exposed to an external electromagnetic field with circular (or linear) polarization, whose in-plane projection of the electric field is modulated along $x$ direction. The modulation of the time-dependent electric field is induced by a special mask, which consists in metallic strips with the period $d$. (b) Profile of the system together with the spatial dependence of the critical temperature. The critical temperature of the etched regions $T_{c2}$ is lower than the critical temperature of the unetched regions $T_{c1}$.
• Figure 2: Normalized spectra of the Hall electric current density in the case of circular (red) and linear (black) polarization of the EM field: The dependencies of the dimensionless functions $\mathcal{F}_{\rm cp}$ from Eq. (\ref{['current_circ']}) (red) and $\mathcal{F}_{\rm ln}$ from Eq. (\ref{['function_circ']}) (black) on the dimensioless frequency $\tilde{\omega}\equiv \omega\tau_{GL}=\pi\omega/8(T-T_{c0})$. Inset: Functions $\mathcal{F}_{\rm cp}(\tilde{\omega})/\tilde{\omega}$ and $\mathcal{F}_{\rm cp}(\tilde{\omega})/\tilde{\omega}^2$.