  Quantum transport properties in molecularly thin perovskite/graphene
heterostructure are experimentally investigated by Shubnikov-de Hass (SdH)
oscillation and photo-resistance spectroscopy. We find an efficient charge
transfer between the perovskite nanosheets and graphene, with a high hole
concentration in graphene of up to $\rm \sim 2.8 \times 10^{13}\ cm^{-2}$. The
perovskite layer also increases Fermi velocity lowering the effective mass of
graphene from expected $\rm \sim 0.12\ m_e$ to $\rm \sim 0.08\ m_e$. Combining
magneto-resistance and density functional theory calculations, we find that the
carrier density in graphene significantly depends on the perovskite termination
at the interface, affecting the charge transfer process and leading to a
coexistence of regions with different doping. We also investigate the
photo-response of the SdH oscillation under illumination. Using
photo-resistance spectroscopy, we find evidence of photo-assisted transport
across the perovskite layer between two graphene electrodes mediated by hot
carriers in perovskite. Our results provide a picture to understand the
transport behavior of 2D perovskite/graphene heterostructure and a reference
for the controlled design of interfaces in perovskite optoelectronic devices.
