A CALCULABLE QUANTUM CAPACITANCE

The idea of a quantum capacitance is introduced explicitly via the generally valid operational definition based on the quadratic charging energy. The direct quantum capacitance C-Q per unit area for a strictly two-dimensional metallic bilayer is shown to be 1/pi a(B), where a(B) = the Bohr radius. This calculable quantum capacitance acts in series with the usual classical capacitance C-cl = epsilon/4 pi d, and is independent of the bilayer spacing d, i.e. it has a universal value. Thus, in most cases C-Q much greater than C-cl and is, therefore, ineffective. However, for the ultrathin bi/multilayers now grown routinely epitaxially, as also for the bi/multilayers inherent to the layered high-T-c superconductors, we can have CQ less than or equal to C-cl, making C-Q dominant. Some possible observable effects are pointed out.