A calculable quantum capacitance

Abstract

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 l/πa_B, where a_B = the Bohr radius. This calculable quantum capacitance acts in series with the usual classical capacitance C_cl = ε/4πd, and is independent of the bilayer spacing d, i.e. it has a universal value. Thus, in most cases C_Q»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 C_Q ≤C_cl making C_Q dominant. Some possible observable effects are pointed out.