Spin-valley dependent double Andreev reflections in the proximitized graphene/superconductor junction

We study the Andreev reflections and the quantum transport in the proximitized graphene/superconductor junction. The proximitized graphene possesses the pseudospin staggered potential and the intrinsic spin-orbit coupling induced by substrate, which are responsible for the spin-valley dependent double Andreev reflections and the anomalous transport properties in the junction. The pure specular Andreev reflection can happen in the superconducting gap for the $K\uparrow$ and $K'\downarrow$ electrons while the pure retro-Andreev reflection happens for the $K\downarrow$ and $K'\uparrow$ electrons. The coexisting two types of Andreev reflections related to the fixed spin-valley indices strongly depend on the chemical potential of the proximitized graphene. The condition of the emergence of the specific type of Andreev reflection for the electrons with the fixed spin-valley index is clarified. The spin-valley dependent Andreev reflections bring about the peculiar conductance spectra of the junction, which can help determine the values of the pseudospin staggered potential and the intrinsic spin-orbit coupling induced in graphene. Hence, our research results not only provide an experimental method to detect the induced potential and coupling in graphene but also establish the foundation of the superconductor electronics based on the spin-valley indices.