Microscopic theory of supercurrent suppression by gate-controlled surface depairing

Recently, gate-mediated supercurrent suppression in superconducting nanobridges has been reported in many experiments. This could be either a direct or an indirect gate effect. The microscopic understanding of this observation has not been clear until now. Using the quasiclassical Green's function method, we show that a small concentration of magnetic impurities at the surface of the bridges can significantly help to suppress superconductivity and hence the supercurrent inside the systems while a gate field is applied. This is because the gate field can enhance the depairing through the exchange interaction between the magnetic impurities at the surface and the superconductor. We also obtain a symmetric suppression of the supercurrent with respect to the gate field, a signature of a direct gate effect. We discuss the parameter range of applicability of our model and how it is able to qualitatively capture the main aspects of the experimental observations. Future experiments can verify our predictions by modifying the surface with magnetic impurities.