Abstract
We explore quantum effects of capacitance in nano-scale systems, by using a first-principles calculation of a carbon nanotube (CNT) capacitor. We show that the capacitance exhibits two principal quantum effects: First, the capacitance shows a large bias dependence, reflecting the density of states structure of the CNT with the divergent-type Van-Hove singularities peculiar to quasi-one dimensional systems. Second, the capacitance is larger than what the classical electromagnetism predicts with the tube-wall radius, according to a quantum spill of the stored charge density from the tube wall. We argue that these two quantum effects in the capacitance become more prominent when the system size gets smaller, which will open a new possibility for a design and control of nanometer scale devices.
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