Capacitance and compressibility of heterostructures with strong electronic correlations

Strong electronic correlations related to a repulsive local interaction suppress the electronic compressibility in a single-band model, and the capacitance of a corresponding metallic film is directly related to its electronic compressibility. Both statements may be altered significantly when two extensions to the system are implemented which we investigate here: (i) we introduce an attractive nearest-neighbor interaction $V$ as antagonist to the repulsive onsite repulsion $U$, and (ii) we consider nanostructured multilayers (heterostructures) assembled from two-dimensional layers of these systems. We determine the respective total compressibility $\ensuremath{\kappa}$ and capacitance $C$ of the heterostructures within a strong coupling evaluation, which builds on a Kotliar-Ruckenstein slave-boson technique. Whereas the capacitance $C(n)$ for electronic densities $n$ close to half-filling is suppressed, illustrated by a correlation induced dip in $C(n)$, it may be appreciably enhanced close to a van Hove singularity. Moreover, we show that the capacitance may be a nonmonotonic function of $U$ close to half-filling for both attractive and repulsive $V$. The compressibility $\ensuremath{\kappa}$ can differ from $C$ substantially, as $\ensuremath{\kappa}$ is very sensitive to internal electrostatic energies which in turn depend on the specific setup of the heterostructure. In particular, we show that a capacitor with a polar dielectric has a smaller electronic compressibility and is more stable against phase separation than a standard nonpolar capacitor with the same capacitance.