We present a review of the electronic compressibility of monolayer and bilayer graphene. We focus on describing theoretical calculations of the effects of electron--electron interactions and various types of disorder, and also give a summary of current experiments and describe which aspects of theory they support. We also include a full analysis of all commonly-used contributions to the tight-binding Hamiltonian of bilayer graphene and their effects on the compressibility.
@article{arxiv.1202.5313,
title = {The compressibility of graphene},
author = {D. S. L. Abergel},
journal= {arXiv preprint arXiv:1202.5313},
year = {2015}
}