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 [B. Skinner and B. I. Shklovskii, Phys. Rev. B 82, 155111 (2010)] argued that when the effective Bohr radius a(B) of the 2DEG satisfies a(B) << d, one can achieve C >> C-g at a 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 concentrations if there is a strong perpendicular magnetic field. DOI: 10.1103/PhysRevB.87.035409