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

## TL;DR

This paper investigates the mechanisms behind capacitance enhancement beyond classical limits in capacitors with free-electron-like electrodes, revealing new factors influencing negative electron compressibility through first-principles calculations.

## Contribution

It identifies previously overlooked mechanisms affecting negative capacitance in realistic physical systems, expanding understanding beyond traditional semiconductor quantum wells.

## Key findings

- New mechanisms related to electronic cloud displacement and multiband effects influence negative capacitance.
- Care must be taken when applying existing theories to different material systems.
- First-principles calculations reveal additional sources of capacitance enhancement in weak confinement regimes.

## Abstract

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