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Capacitance of graphene nanoribbons

机译：石墨烯纳米带的电容

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摘要

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 noninter-acting 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.
机译：我们提出了石墨烯纳米带（GNR）的栅极静电以及经典电容和量子电容的分析理论，并将其与基于Hartree逼近中的紧束缚p轨道哈密顿量的精确自洽数值计算进行了比较。我们证明分析理论与精确的计算在质量上（在某些方面是定量的）一致。但是，存在一些重要的差异。为了了解这些差异的根源，我们研究了纳米带中的自洽电子结构和电荷密度分布，并将上述差异与简单静电模型无法捕获GNR的经典栅极静电联系起来。反过来，经典静电的失效可追溯到量子力学效应，与非相互作用电子描述相比，量子力学效应导致自洽电荷分布的显着改变。讨论了电子相互作用在电子结构和GNR电容中的作用。我们的精确数值计算表明，GNR中的密度分布和电势轮廓与常规的分裂栅量子线中的密度分布和电势轮廓在质量上有所不同。同时，GNR中的电子分布和电势分布在质量上与裂开的长满的量子线中的特征相似。最后，我们讨论了从实验数据中对量子电容的实验提取。

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