Electrostatic screening of free charge-neutral dipoles/excitons in two-dimensional media

With the shrinking of dimensionality, Coulomb interaction plays a distinct role in two-dimensional (2D) semiconductors owing to the reduced dielectric screening in the out-of-plane direction. Apart from the dielectric screening, free particles such as carriers and dipoles or excitons can also make a non-negligible contribution to the Coulomb interaction. While the Thomas-Fermi model is effective in describing charge carrier screening in three dimensions, the extent of screening resulting from neutral dipoles or excitons in both two and three dimensions remains quantitatively unclear. Here, we present an analytical solution based on linear response theory, offering a comprehensive depiction of the Coulomb screened potential from charge-neutral dipoles or excitons in both 2D and 3D systems, while the free dipole screening effect is much stronger in the 2D case than that in the 3D case. Using the derived screened Coulomb potential, we estimate the exciton binding energy shift arising from the mutual exciton screening effect, which is found to be an order of magnitude larger than that due to exchange-driven exciton-exciton interaction, yielding excellent agreement with the experimental observations. Our work provides a practical and insightful framework for directly analyzing and evaluating Coulomb interaction strength in an excitonic system in atomically thin materials, with implications for the design of electronic and optoelectronic devices.