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 on-site repulsion U , and (ii) we consider nano-structured multilayers (heterostructures) assembled from two-dimensional layers of these systems. We determine the respective total compressibility κ 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 non-monotonic function of U close to half-filling for both attractive and repulsive V . The compressibility κ can differ from C substantially, as κ is very sensitive to internal electrostatic energies which in turn depend on the specific set-up 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 non-polar capacitor with the same capacitance.

Oxide heterostructures with polar films display special electronic properties, such as the electronic reconstruction at their internal interfaces with the formation of two-dimensional metallic states. Moreover, the electrical field from the polar layers is inversion-symmetry breaking and generates a Rashba spin-orbit coupling (RSOC) in the interfacial electronic system. We investigate the quantum capacitance of a heterostructure in which a sizeable RSOC at a metallic interface is controlled by the electric field of a surface electrode. Such a structure is, for example, given by a LaAlO3 film on a SrTiO3 substrate which is gated by a top electrode. Such heterostructures can exhibit a strong enhancement of their capacitance [1]. The capacitance is related to the electronic compressibility of the heterostructure, but the two quantities are not equivalent. In fact, the transfer of charge to the interface controls the relation between capacitance and compressibility. We find that due to a strong RSOC, the quantum capacitance can be larger than the classical geometric value. However, in contrast to the results of recent investigations [9-11] the compressibility does not become negative for realistic parameter values for LaAlO3/SrTiO3 and, therefore, we find that no phase-separated state is induced by the strong RSOC at these interfaces.

Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility-ultimately signalling charge instability and phase separation-and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter F s 0 are presented, whereby the positivity of F s 0 − 1 constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter t shifts their positions and produces a tendency towards charge instability even for low filling whereas the t -controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction V is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction U , at densities far from half filling.

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