Giant capacitance of a plane capacitor with a two-dimensional electron gas in a magnetic field

TL;DR

This paper demonstrates that a strong perpendicular magnetic field can induce giant capacitance in a two-dimensional electron gas-based plane capacitor, even when the effective Bohr radius exceeds the electrode separation.

Contribution

It reveals that magnetic fields can significantly enhance capacitance beyond geometric limits in 2DEG systems, including graphene, regardless of the Bohr radius size.

Findings

Capacitance exceeds geometric limit at low electron concentration.

Magnetic field induces giant capacitance in 2DEG systems.

Effect applies to graphene with effectively infinite Bohr radius.

Abstract

If a clean two-dimensional electron gas (2DEG) with small concentration $n$ comprises one (or both) electrodes 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. A recent paper [1] argued that when the effective Bohr radius $a_B$ of the 2DEG satisfies $a_B << d$, one can achieve $C >> C_g$ at low concentration $nd^2 << 1$. Here we show that even for devices with $a_B > d$, including graphene, for which $a_B$ is effectively infinite, one also arrives at $C >> C_g$ at low electron concentration if there is a strong perpendicular magnetic field.