Quantum capacitance of double-layer graphene

We study the ground-state properties of a double-layer graphene system with the Coulomb interlayer electron-electron interaction modeled within the random-phase approximation. We first obtain an expression of the quantum capacitance of a two-layer system. In addition, we calculate the many-body exchange-correlation energy and quantum capacitance of the hybrid double-layer graphene system at zero temperature. We show an enhancement of the majority density layer thermodynamic density of states owing to an increasing interlayer interaction between two layers near the Dirac point. The quantum capacitance near the neutrality point behaves like a square root of the total density $\ensuremath{\alpha}\sqrt{n}$ where the coefficient $\ensuremath{\alpha}$ decreases by increasing the charge-density imbalance between two layers. Furthermore, we show that the quantum capacitance changes linearly by the gate voltage. Our results can be verified by current experiments.