O cálculo da capacitância em sistemas quânticos: uma abordagem por primeiros princípios e aplicações ao estudo de nanoestruturas

Abstract

Classically, the capacitance of a system is determined by the ratio between a fixed amount of charge and the difference in the electrostatic potential required in the charging process. However, in quantum systems, there are additional energy terms which have to be takeninto account in the capacitance calculation. In this work, we perform a study related to the determination of this property in nanostructures within the formalism of the Density Functional Theory (DFT). We analyze the two main approaches in the literature, distinguishing between the classical and quantum contributions for the total capacitance, and we apply them to the calculation of this property in nanostructured materials, suchas fullerenes. We investigate the changes in the capacitance when the material is placed in the presence of gases, which may be relevant to the construction of capacitive sensors. We also try to establish a correspondence with the physics of quantum dots.