### 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 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.

Original language | English |
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Article number | eaay8409 |

Journal | Science Advances |

Volume | 6 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2020 |

### All Science Journal Classification (ASJC) codes

- General

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## Cite this

*Science Advances*,

*6*(11), [eaay8409]. https://doi.org/10.1126/sciadv.aay8409