First-principles quantum corrections for carrier correlations in double-layer two-dimensional heterostructures

We present systematic ab initio calculations of the charge carrier correlations between adjacent layers of two-dimensional materials in the presence of both charged impurity and strain disorder potentials using the examples of monolayer and bilayer graphene. Our analysis yields unambiguous first-principles quantum corrections to the Thomas-Fermi densities for interacting two-dimensional systems described by orbital-free density functional theory. Specifically, using density-potential functional theory, we find that quantum corrections to the quasiclassical Thomas-Fermi approximation have to be taken into account even for heterostructures of mesoscopic size. In order for the disorder-induced puddles of electrons and holes to be anticorrelated at zero average carrier density for both layers, the strength of the strain potential has to exceed that of the impurity potential by at least a factor of ten, with this number increasing for smaller impurity densities. Furthermore, our results show that quantum corrections have a larger impact on puddle correlations than exchange does, and they are necessary for properly predicting the experimentally observed Gaussian energy distribution at charge neutrality.