Compressibility of graphene

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.

10 pages, 7 figures, RevTeX

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Cited by in corpus (15)

• The electronic properties of bilayer graphene
• Disorder-induced temperature-dependent transport in graphene: Puddles, impurities, activation, and diffusion
• The role of charge traps in inducing hysteresis: capacitance - voltage measurements on top gated bilayer graphene
• Capacitance of Graphene Bilayer as a Which-Layer Probe
• Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
• Temperature-dependent compressibility in graphene and two-dimensional systems
• Density fluctuation effects on the exciton condensate in double layer graphene
• Quantum capacitance and compressibility of graphene: The role of Coulomb interactions
• Quantum capacitance and Landau parameters of massless Dirac fermions in graphene
• Temperature-dependent many-body effects in Dirac-Weyl materials: Interacting compressibility and quasiparticle velocity
• Comparison of microscopic models for disorder in bilayer graphene: Implications for the density of states and the optical conductivity
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• Quantum capacitance of an HgTe quantum well as an indicator of the topological phase
• The compressibility of graphene
• Dynamic Bandstructure and Capacitance Effects in Scanning Tunneling Spectroscopy of Bilayer Graphene