Anomalously large capacitance of a plane capacitor with a two-dimensional electron gas

TL;DR

This paper develops a theory explaining how Coulomb correlations in a two-dimensional electron gas can cause the capacitance of a plane capacitor to significantly exceed its geometric value, especially at low electron densities.

Contribution

It introduces a comprehensive theory for capacitance enhancement in 2DEG systems across all regimes of electron-electron correlation, including the regime where $nd^2 << 1$, and matches experimental results without adjustable parameters.

Findings

Capacitance can be up to 4d/a times larger than geometric capacitance.

Correlations between opposite electrodes are crucial at low $nd^2$ regimes.

The theory aligns well with recent experimental observations.

Abstract

In electronic devices where a two-dimensional electron gas (2DEG) comprises one or both sides of a plane capacitor, the resulting capacitance $C$ can be larger than the "geometric capacitance" $C_g$ determined by the physical separation $d$ between electrodes. This larger capacitance is known to result from the Coulomb correlations between individual electrons within the low density 2DEG, which lead to a negative thermodynamic density of states (negative compressibility). Experiments on such systems generally operate in the regime where the average spacing between electrons $n^{-1/2}$ in the 2DEG is smaller than $d$, and these experiments observe $C > C_g$ by only a few percent. A recent experiment [1], however, has observed $C$ larger than $C_g$ by almost 40% while operating in the regime $nd^2 << 1$. In this paper we argue that at $nd^2 << 1$ correlations between the electronic charge of opposite electrodes become important. We develop a theory of the capacitance for the full range of $nd^2$. We show that, in the absence of disorder, the capacitance can be $4d/a$ times larger than the geometric value, where $a << d$ is the electron Bohr radius. Our results compare favorably with the experiment of Ref. [1] without the use of adjustable parameters.