The electronic thickness of graphene

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P. Rickhaus, M.-H. Liu,M. Kurpas, A. Kurzmann, Y. Lee, H. Overweg, M. Eich, R. Pisoni, T. Taniguchi,
K. Watanabe, K. Richter, K. Ensslin, T. Ihn

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Science Advances

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 θ = 22° 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 ≈ 2.6 Å. In a second experiment, we map out the entire density range with a Fabry-Pérot resonator. We can precisely measure the Fermi wavelength λ in each layer, showing that the layers are decoupled. Our findings are reproduced using tight-binding calculations.

 

https://advances.sciencemag.org/content/6/11/eaay8409
https://epub.uni-regensburg.de/40498/