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" C_g determined by the physical separation d between electrodes. A recent paper argued that when the effective Bohr radius a_B of the 2DEG satisfies a _Bâ‰d, one can achieve Câ‰C_g at a low concentration nd2â‰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 Câ‰C_g at low electron concentrations if there is a strong perpendicular magnetic field.