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With the shrink of dimensionality, Coulomb interaction displays a distinctrole owing to the reduced dielectric screening in out-of-plane direction. Apartfrom the dielectric screening, the free charge carriers and/or dipoles can alsomake nonnegligible contribution to Coulomb interaction. While the Thomas Fermimodel is effective in describing charge carrier screening in three dimensions,the extent of screening to two-dimension resulting from charge-neutral dipolesand carriers remains quantitatively unclear. To address this gap, we present asimple analytical solution based on linear response theory, offering acomprehensive depiction of the Coulomb screened potential in both 2D and 3Dsystems, where screening effects from both charge carriers and charge-neutraldipoles are addressed. Our work provides a handy tool for directly analysingand evaluating Coulomb interaction strength in atomically thin materials andparticularly in the context of electronic and optoelectronic engineering. As ademonstration, we utilize the derived modified Coulomb potential for theexciton system to estimate the exciton binding energy variation arising fromexciton density fluctuation and the temperature dependent excitonpolarizability, yielding excellent agreement with the experimental andcomputational findings.

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