Superconducting Photocurrent and Light Enriched Supercurrent Phase Relation

Noncentrosymmetric superconductors are expected to exhibit DC photocurrents even for irradiation frequencies below the superconducting gap. Such superconducting photocurrent are non-dissipative and track the quantum geometry of the superconducting state. Here we argue that superconducting photocurrent drives changes to the constitutive superconducting current phase relation (CPR) manifesting in a light controlled inductive response as well as altering the critical current. For chiral incident light, we find that superconducting photocurrent can transform reciprocal CPR into a non-reciprocal CPR producing a non-reciprocal inductance and light-controlled superconducting diode effect. These provide a protocol for measuring superconducting photocurrent and new tools for mapping the quantum geometry and order parameter of superconductors.