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

Brian Skinner; B. I. Shklovskii

doi:10.1103/PhysRevB.82.155111

paper

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

arXiv:1007.5308 · doi:10.1103/PhysRevB.82.155111

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 $n d^{2} << 1$ . In this paper we argue that at $n d^{2} << 1$ correlations between the electronic charge of opposite electrodes become important. We develop a theory of the capacitance for the full range of $n d^{2}$ . We show that, in the absence of disorder, the capacitance can be $4 d / a$ 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.

8 pages, 6 figures; revised discussion of the zero density limit; some typos fixed

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

Abstract

References in corpus (7)

Cited by in corpus (44)