Odd momentum pairing and superconductivity in vertical graphene heterostructures

Vertical graphene heterostructures made up of graphene layers separated by BN spacers allow for novel ways of tuning the interactions between electrons. We study the possibility of electron pairing mediated by modified repulsive interactions. Long range intravalley and short range intervalley interactions give rise to different anisotropic phases. We show that a superconducting state with gaps of opposite signs in different valleys, an odd momentum pairing state, can exist above carrier densities of $5-10 \times 10^{13} {\rm cm}^{-2}$. The dependence of the transition temperature on the different parameters of the devices is studied in detail.