2009/07/06 by A. A. Shylau, Jarosław W. Kłos, J. W. Klos +2 · 3 citations
Engineering · Materials Science · Physics and Astronomy · #Graphene research and applications #Molecular Junctions and Nanostructures #Quantum and electron transport phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.80.205402
published as Phys. Rev. B 80, 205402 (2009) · 9 pages, 5 figures, submitted to PRB
arxiv created 2009/07/06 · openalex publication_date 2009/11/04 · arxiv updated 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We present an analytical theory for the gate electrostatics and the classical and quantum capacitance of the graphene nanoribbons (GNRs) and compare it with the exact self-consistent numerical calculations based on the tight-binding p-orbital Hamiltonian within the Hartree approximation. We demonstrate that the analytical theory is in a good qualitative (and in some aspects quantitative) agreement with the exact calculations. There are however some important discrepancies. In order to understand the origin of these discrepancies we investigate the self-consistent electronic structure and charge density distribution in the nanoribbons and relate the above discrepancy to the inability of the simple electrostatic model to capture the classical gate electrostatics of the GNRs. In turn, the failure of the classical electrostatics is traced to the quantum mechanical effects leading to the significant modification of the self-consistent charge distribution in comparison to the noninteracting electron description. The role of electron-electron interaction in the electronic structure and the capacitance of the GNRs is discussed. Our exact numerical calculations show that the density distribution and the potential profile in the GNRs are qualitatively different from those in conventional split-gate quantum wires; at the same time, the electron distribution and the potential profile in the GNRs show qualitatively similar features to those in the cleaved-edge overgrown quantum wires. Finally, we discuss an experimental extraction of the quantum capacitance from experimental data.