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

## TL;DR

This paper uses first-principles calculations to analyze quantum corrections to charge carrier correlations in two-dimensional heterostructures, revealing the importance of quantum effects in predicting electron-hole puddle behaviors.

## Contribution

It provides the first unambiguous first-principles quantum corrections to Thomas-Fermi densities in 2D heterostructures using density-potential functional theory.

## Key findings

- Quantum corrections significantly affect puddle correlations.
- Strain potential must exceed impurity potential by tenfold for anti-correlation.
- Quantum effects are crucial for matching experimental energy distributions.

## Abstract

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. For the first time, 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 quasi-classical 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 anti-correlated 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.