Electronic compressibility of a graphene bilayer

TL;DR

This paper calculates the electronic compressibility of a graphene bilayer considering electron-electron interactions, revealing unique non-monotonic behavior due to the system's chiral nature and competing intra- and inter-band effects.

Contribution

It provides the first detailed Hartree-Fock analysis of compressibility in graphene bilayers highlighting the role of chirality and interaction competition.

Findings

Compressibility differs from 2D electron gas and semiconductors.

Non-monotonic compressibility as a function of carrier density.

Competition between intra-band and inter-band interactions.

Abstract

We calculate the electronic compressibility arising from electron-electron interactions for a graphene bilayer within the Hartree-Fock approximation. We show that, due to the chiral nature of the particles in this system, the compressibility is rather different from those of either the two-dimensional electron gas or ordinary semiconductors. We find that an inherent competition between the contributions coming from intra-band exchange interactions (dominant at low densities) and inter-band interactions (dominant at moderate densities) leads to a non-monotonic behavior of the compressibility as a function of carrier density.