Intravalley Andreev reflection in the multi-terminal device with Y-shaped Kekul\'{e} graphene superlattices

Using the tight-binding model, a multi-terminal superconductor(S) device is proposed, where the structures of the center region are primitive grpahene(G) and Y-shaped Kekul\'{e} graphene superlattice(GS), respectively. The intravalley Andreev reflection is studied in this model through the utilization of the non-equilibrium Green's function method. In the G/S device, due to the time-reverse symmetry the dominant process of Andreev reflection is intervalley reflection. In a three-terminal GS/S device, it has been observed that the coefficient of intravalley Andreev reflection can surpass that of intervalley reflection in crossed Andreev reflection. This is attributed to the coupling between valleys K and -K within the first Brillouin zone, resulting in enhanced intervalley scattering. The valley-dependent transport of Andreev reflection can be influenced by the phase difference between superconductor terminals. The valley polarization of the local Andreev reflection and the crossed Andreev reflection could be controlled by adjusting the structure of the central region.