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 CQ per unit area for a strictly two-dimensional metallic bilayer is shown to be 1/παB where αB = the Bohr radius. This calculable quantum capacitance acts in series with the usual classical capacitance Ccl = ε/4πd, and is independent of the bilayer spacing d, i.e., it has a universal value. Thus, in most cases CQ >> Ccl 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-Tc superconductors, one can have CQ ≤ Ccl, making CQ dominant. Some possible observable effects are pointed out. (author). 5 refs