# Quantum capacitance of double-layer graphene

## TL;DR

This paper investigates the quantum capacitance of double-layer graphene, revealing how interlayer interactions influence density-of-states and capacitance behavior near the neutrality point, with results verifiable experimentally.

## Contribution

It provides a theoretical expression for quantum capacitance in double-layer graphene considering Coulomb interactions within the random phase approximation.

## Key findings

- Quantum capacitance scales as sqrt of total density near neutrality point.
- Interlayer interaction enhances the density-of-states in the majority layer.
- Quantum capacitance varies linearly with gate voltage.

## Abstract

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 square root of the total density, $\alpha \sqrt{n}$, where the coefficient $\alpha$ 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.