Frequency dependent capacitance and plasmon excitations in a coherent parallel-plate capacitor

We report the theoretical investigations of frequency-dependent capacitance in a coherent parallel-plate capacitor. It is found that the capacitance strongly depends on frequency and is complex at finite frequency. An interesting result is that in the frequency dependence of capacitance, a peak in the imaginary part of capacitance corresponds to the minimum of the real part and is related to a plasmonlike excitation, which is of damping and has a short lifetime. We also discussed the size effect of the capacitor and find that the capacitance approaches geometric capacitance when the distance between two plates of the capacitor is very large.