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 a low concentration n comprises one electrode of a plane capacitor, the resulting capacitance C can be higher than the ``geometric capacitance'' Cg determined by the physical separation d between electrodes. A recent paper [B. Skinner and B. I. Shklovskii, Phys. Rev. B 82, 155111 (2010)] argued that when the effective Bohr radius aB of the 2DEG satisfies aBd, one can achieve CCg at a low concentration nd²1. Here we show that even for devices with aB>d, including graphene, for which aB is effectively infinite, one also arrives at CCg at low electron concentrations if there is a strong perpendicular magnetic field.