  High-T_c superconductors confined to two dimension exhibit novel physical
phenomena, such as superconductor-insulator transition. In the
Bi_2Sr_2CaCu_2O_8+x (Bi2212) model system, despite extensive studies, the
intrinsic superconducting properties at the thinness limit have been difficult
to determine. Here we report a method to fabricate high quality single-crystal
Bi2212 films down to half-unit-cell thickness in the form of graphene/Bi2212
van der Waals heterostructure, in which sharp superconducting transitions are
observed. The heterostructure also exhibits a nonlinear current-voltage
characteristic due to the Dirac nature of the graphene band structure. More
interestingly, although the critical temperature remains essentially the same
with reduced thickness of Bi2212, the slope of the normal state T-linear
resistivity varies by a factor of 4-5, and the sheet resistance increases by
three orders of magnitude, indicating a surprising decoupling of the normal
state resistance and superconductivity. The developed technique is versatile,
applicable to investigate other two-dimensional (2D) superconducting materials.
