Electrodynamic models of 2D materials: can we match thin film and single sheet approaches?

TL;DR

This paper compares the electromagnetic modeling approaches of 2D materials as single sheets versus thin films, emphasizing the importance of anisotropy and effective thickness in accurately predicting optical responses.

Contribution

It provides analytical relations between the two modeling approaches and highlights how anisotropy and thickness choices influence the predicted optical properties.

Findings

Thin film and single sheet models can be matched by adjusting thickness and anisotropy parameters.

Anisotropy significantly affects the optical response predictions.

The choice of effective thickness in thin film models is crucial for accurate modeling.

Abstract

The electromagnetic properties of 2D materials are modeled either as single sheets with a surface susceptibility or conductivity, or as thin films of finite thickness with an effective permittivity. Their intrinsic anisotropy, however, has to be fully described to reliably predict the optical response of systems based on 2D materials or to unambiguously interpret experimental data. In the present work, we compare the two approaches within the transfer matrix formalism and provide analytical relations between them. We strongly emphasize the consequences of the anisotropy. In particular, we demonstrate the crucial role of the choice of the thin film's effective thickness compared with the parameters of the single sheet approach and therefore the computed properties of the 2D material under study. Indeed, if the isotropic thin film model with very low thickness is similar to an anisotropic single sheet with no out-of-plane response, with larger thickness it matches with a single sheet with isotropic susceptibility, in the reasonable small phase condition. We illustrate our conclusions on extensively studied experimental quantities such as transmittance, ellipsometry and optical contrast, and we discuss similarities and discrepancies reported in the literature when using single sheet or thin film models.