Capacitance of graphene nanoribbons

A. A. Shylau, J. W. Kłos, and I. V. Zozoulenko
Phys. Rev. B 80, 205402 – Published 4 November 2009

Abstract

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.

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  • Received 6 July 2009

DOI:https://doi.org/10.1103/PhysRevB.80.205402

©2009 American Physical Society

Authors & Affiliations

A. A. Shylau1, J. W. Kłos1,2, and I. V. Zozoulenko1

  • 1Solid State Electronics, ITN, Linköping University, 601 74 Norrköping, Sweden
  • 2Surface Physics Division, Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan, Poland

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Issue

Vol. 80, Iss. 20 — 15 November 2009

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