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We consider a planar two-dimensional system between two media with differentdielectric constants and in the presence of a third dielectric medium separatedby a nonplanar interface. Extending a perturbative method for solving Poisson'sequation, developed by Clinton, Esrick, and Sacks [Phys. Rev. B, 31, 7540(1985)], in the presence of nonplanar conducting boundaries to the situationproposed here, we obtain, up to the first order in terms of the function whichdefines the nonplanar interface, the effective potential, the effectiveelectrostatic field, the effective dielectric constant for the planar 2Dsystem, and the effective external field acting in-plane in the 2D system.Implications of the results to properties of 2D systems are discussed. In thelimit of planar surfaces, vacuum-dielectric or vacuum-conducting media, ourresults are in agreement with those found in the literature.

Two-dimensional materials in the presence of nonplanar interfaces