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The so-called negative electron compressibility refers to the lowering of thechemical potential of a metallic system when the carrier density increases.This effect has often been invoked in the past to explain the enhancement ofthe capacitance beyond the classical limits in capacitors with two-dimensionalelectron gases as electrodes. Based on experiments on strongly confinedsemiconductor quantum wells (QWs), it has been traditionally ascribed to theelectron exchange energy as the main driving force. Recent research, however,has revealed that analogous effects can occur in other classes of materialssystems, such as polar oxide interfaces, whose characteristics drasticallydepart from those of the previously considered cases. To rationalize these newresults, it is necessary to revisit the established theory of confined electrongases, and test whether its conclusions are valid beyond the specifics ofsemiconductor-based QWs. Here we find, based on first-principles calculationsof jellium slabs, that one must indeed be very careful when extrapolatingexisting results to other realistic physical systems. In particular, weidentify a number of additional, previously overlooked mechanisms (e.g.,related to the displacement of the electronic cloud and to the multibandstructure of the delocalized gas), that enter into play and become new sourcesof negative capacitance in the weak-confinement regime. Our detailed analysisof these emerging contributions, supported by analytic models and multiple testcases, will provide a useful guidance in the ongoing quest for nanometriccapacitors with enhanced performance.

Novel mechanisms to enhance the capacitance beyond the classical limits in capacitors with free-electron-like electrodes