Compressibility of graphene

TL;DR

This paper develops a theoretical framework for understanding the compressibility and quantum capacitance of disordered monolayer and bilayer graphene, incorporating full band structure and disorder effects, and compares predictions with experimental data.

Contribution

It introduces two models for disorder averaging in graphene and evaluates their accuracy against experimental results, especially in gapped bilayer graphene.

Findings

Density of states averaging fails for gapped systems.

Both models work well for gapless graphene.

The model predicts the size of the band gap under various gate voltages.

Abstract

We develop a theory for the compressibility and quantum capacitance of disordered monolayer and bilayer graphene including the full hyperbolic band structure and band gap in the latter case. We include the effects of disorder in our theory, which are of particular importance at the carrier densities near the Dirac point. We account for this disorder statistically using two different averaging procedures: first via averaging over the density of carriers directly, and then via averaging in the density of states to produce an effective density of carriers. We also compare the results of these two models with experimental data, and to do this we introduce a model for inter-layer screening which predicts the size of the band gap between the low-energy conduction and valence bands for arbitary gate potentials applied to both layers of bilayer graphene. We find that both models for disorder give qualitatively correct results for gapless systems, but when there is a band gap at charge neutrality, the density of states averaging is incorrect and disagrees with the experimental data.