The electronic thickness of graphene.

Rickhaus, Peter; Liu, Ming-Hao; Kurpas, Marcin; Kurzmann, Annika; Lee, Yongjin; Overweg, Hiske; Eich, Marius; Pisoni, Riccardo et al. · Sci Adv · 2020

basic_science · Level V

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Abstract

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 <i>C</i> <sub>m</sub> and is therefore suited to extract <i>C</i> <sub>m</sub>. We explain the large observed value of <i>C</i> <sub>m</sub> by considering the finite dielectric thickness <i>d</i> <sub>g</sub> of each graphene layer and determine <i>d</i> <sub>g</sub> ≈ 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.