The electronic thickness of graphene

When two dimensional crystals are atomically close, their finite thickness becomes relevant. Using transport measurements, we investigate the electrostatics of two graphene layers, twisted by theta = 22 degrees such that the layers are decoupled by the huge momentum mismatch between the K and K' points of the two layers. We observe a splitting of the zero-density lines of the two layers with increasing interlayer energy difference. This splitting is given by the ratio of single-layer quantum capacitance over interlayer capacitance C-m and is therefore suited to extract C-m. We explain the large observed value of C-m by considering the finite dielectric thickness d(g) of each graphene layer and determine d(g) approximate to 2.6 angstrom. In a second experiment, we map out the entire density range with a Fabry-Perot resonator. We can precisely measure the Fermi wavelength lambda in each layer, showing that the layers are decoupled. Our findings are reproduced using tight-binding calculations.