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

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.