Coulomb potential screening via charged carriers and charge-neutral dipoles/excitons in two-dimensional case

With the shrinking of dimensionality, Coulomb interactions play a distinct role in two-dimensional (2D) semiconductors owing to the reduced dielectric screening in the out-of-plane direction. Apart from dielectric screening, free charge carriers and/or dipoles can also make a non-negligible contribution to Coulomb interaction. While the Thomas-Fermi model is effective in describing charge carrier screening in three dimensions, the extent of screening to two dimensions resulting from charge carriers and charge-neutral dipoles remains quantitatively unclear. Herein, we present an analytical solution based on linear response theory, offering a comprehensive depiction of the Coulomb screened potential in both 2D and 3D systems, where screening effects from both charge carriers and charge-neutral dipoles are addressed. Our work provides a useful and handy tool for directly analysing and evaluating Coulomb interaction strength in atomically thin materials, particularly in the context of electronic and optoelectronic engineering. As a demonstration, we utilized the derived modified Coulomb potential for the exciton system in 2D semiconductors to estimate the exciton binding energy variation arising from the exciton density fluctuation and temperature-dependent exciton polarizability, yielding excellent agreement with the computational and experimental findings.