# The Electronic Thickness of Graphene

## TL;DR

This study measures the effective electronic thickness of graphene layers by analyzing electrostatic coupling and quantum capacitance, revealing a finite dielectric thickness and decoupled layers with large Fermi wavelengths, supported by experimental and theoretical results.

## Contribution

It introduces a method to determine the finite dielectric thickness of graphene layers through electrostatic measurements and confirms the decoupled nature of twisted graphene layers with large Fermi wavelengths.

## Key findings

- Measured dielectric thickness of graphene as 2.6 Å.
- Demonstrated decoupling of layers with large Fermi wavelengths.
- Reproduced results with tight-binding calculations.

## Abstract

The van-der-Waals stacking technique enables the fabrication of heterostructures, where two conducting layers are atomically close. In this case, the finite layer thickness matters for the interlayer electrostatic coupling. Here we investigate the electrostatic coupling of two graphene layers, twisted by 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 and is therefore suited to extract C. We explain the large observed value of C by considering the finite dielectric thickness d of each graphene layer and determine d=2.6 Angstrom. In a second experiment we map out the entire density range with a Fabry-P\'erot resonator. We can precisely measure the Fermi-wavelength in each layer, showing that the layers are decoupled. We find that the Fermi wavelength exceeds 600nm at the lowest densities and can differ by an order of magnitude between the upper and lower layer. These findings are reproduced using tight-binding calculations.