Correlation energy of the two-dimensional homogeneous electron gas with screened Coulomb potential

Many interesting electronic states have been observed at semiconductor heterojunctions, including those formed by transition metal dichalcogenide (TMD) bilayers with a moiré potential. In experiments, metallic gates are often used to manipulate the electric fields and charge density. However, these gates also screen the Coulomb interaction between the electrons and can invalidate existing density functionals parameterized for an isolated 2DEG. In this work, we perform diffusion Monte Carlo and numerical effective field theory calculations on the 2DEG subjected to symmetric-gate screening across a range of densities and gate distances. The resulting correlation energy is used to parameterize a local spin density approximation (LSDA) functional. Our fitting form incorporates the analytic expression from perturbation in both the strongly screened and the high-density limits. The LSDA functional will facilitate rapid computational discovery in 2D systems, including moiré materials.