The electronic thickness of graphene.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Nanoscience

Background:

• Finite thickness of 2D crystals becomes significant at atomic proximity.
• Twisted bilayer graphene exhibits unique electronic properties due to interlayer coupling.

Purpose of the Study:

• Investigate the electrostatics of twisted bilayer graphene (θ = 22°).
• Determine the interlayer capacitance (Cm) and dielectric thickness (dg) of individual graphene layers.
• Verify layer decoupling through transport measurements and Fermi wavelength analysis.

Main Methods:

• Transport measurements to observe zero-density line splitting.
• Analysis of quantum capacitance and interlayer capacitance.
• Fabry-Pérot resonator measurements to determine Fermi wavelength.
• Tight-binding calculations for theoretical validation.

Main Results:

• Observed splitting of zero-density lines, proportional to the ratio of quantum capacitance to interlayer capacitance.
• Successfully extracted interlayer capacitance (Cm) and determined graphene dielectric thickness (dg ≈ 2.6 Å).
• Precisely measured Fermi wavelength in each layer, confirming layer decoupling.
• Experimental findings were reproduced by tight-binding calculations.

Conclusions:

• The finite dielectric thickness of graphene layers plays a crucial role in the electrostatics of twisted bilayers.
• The observed phenomena provide a method for extracting interlayer capacitance.
• The study confirms the decoupling of graphene layers in the twisted bilayer system at a specific twist angle.