Two-dimensional materials in the presence of nonplanar interfaces

TL;DR

This paper extends a perturbative method to analyze electrostatic effects in two-dimensional materials near nonplanar dielectric interfaces, providing first-order corrections to potential and field calculations.

Contribution

It introduces a first-order perturbative approach to evaluate electrostatic properties of 2D systems with nonplanar dielectric interfaces, generalizing previous planar interface models.

Findings

Derived effective potential and fields considering nonplanar interfaces.

First-order corrections match known results in planar limit.

Implications for 2D material properties discussed.

Abstract

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