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

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 $n{d}^2<<1$. 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.

arXiv comment6 pages, 5 figures; updated discussion about bilayer systems; added discussion of fractional quantum Hall states

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• The effect of electron dielectric response on the quantum capacitance of graphene in a strong magnetic field
• Theory of a chiral Fermi liquid: general formalism
• Interaction-induced Interlayer Charge Transfer in the Extreme Quantum Limit
• Attraction of indirect excitons in van der Waals heterostructures with three semiconducting layers
• Chemical potential and compressibility of quantum Hall bilayer excitons
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• Chiral Wigner crystal phases induced by Berry curvature
• Bound states of charges on top of graphene in magnetic field
• Interaction-driven capacitance in Graphene electron-hole double layer in the quantum Hall regime
• Correlation effects in the capacitance of a gated carbon nanotube
• Theory of cross quantum capacitance