Electrochemical capacitance of a leaky nanocapacitor

We report a detailed theoretical investigation on electrochemical capacitan ce of a nanoscale capacitor where there is a de coupling between the two co nductors. For this "leaky" quantum capacitor, we have derived general analy tic expressions of the linear and second-order nonlinear electrochemical ca pacitance within a first-principles quantum theory in the discrete potentia l approximation. Linear and nonlinear capacitance coefficients are also der ived in a self-consistent manner without the latter approximation and the s elf-consistent analysis is suitable for numerical calculations. At linear o rder, the full quantum formula improves the semiclassical analysis in the t unneling regime. At nonlinear order that has not been studied before for le aky capacitors, the nonlinear capacitance and nonlinear nonequilibrium char ge show interesting behavior. Our theory allows the investigation of crosso ver of capacitance from a full quantum to classical regimes as the distance between the two conductors is changed. [S0163-1829(99)03548-1].