Ac transport properties of electrons in parallel-plate mesoscopic capacitors in series

In a self-consistent manner by taking into account three aspects: the frequency of the bias, geometry of the capacitor (e.g. plate separation) and the Fermi energy of the system, ac transport properties of electrons in parallel-plate mesoscopic capacitor in series under an bias are discussed. The charge density, the internal characteristic potential caused by electrons interaction and the size-dependent mesoscopic capacitance are calculated. Results show that these quantities are complex number with very small finite imaginary part in mesoscopic scale, and the current conservation is satisfied in our numerical calculation. Moreover, when the plate separation is large enough, the mesoscopic capacitance approaches to the geometric capacitance, and the imaginary parts vanish. When the plate separation is small, there are some differences between them.