  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.
