Optical modelling of single and multilayer 2D materials and heterostructures

TL;DR

This paper introduces a unified optical model for 2D materials and heterostructures that accounts for their finite thickness, enabling consistent analysis of multilayer stacks and monolayers using transfer matrix methods.

Contribution

The authors develop a transfer matrix-based model that bridges the gap between purely surface and thin film approaches, allowing for accurate characterization of 2D materials' volume properties.

Findings

Model aligns with existing ellipsometric data.

Parameters of the model can be derived from experimental measurements.

Provides a consistent framework for multilayer and monolayer systems.

Abstract

Bidimensional materials are ideally viewed as having no thickness, as their name suggests. Their optical response have been previously modelled by a purely bidimensional surface current or by a very thin film with some contradictory results. The advent of multilayer stacks of bidimensional materials and combinations of different materials in vertical van der Waals heterostructures highlights however that these materials have a finite thickness. In this article, we propose a new model that reconciles both approaches and we show how volume properties of stacked bidimensional layers can be calculated from the bidimensional response of each individual layer, and conversely. In our approach, each bidimensionnal layers is surrounded by vacuum and described as a kind of transfer matrix with intrinsic parameters that do not depend on the external medium. This provides a link between continuous thin films and discrete layers. We show how to model heterostructures of bidimensional materials and identify the parameters of the current sheet that represents the bidimensional material in the zero-thickness limit, namely the in-plane surface susceptibility and the out-of-plane displacement susceptibility. We show that our unified model is perfectly compatible with existing ellipsometric data with the same reliability as the existing interface model but with different values of the surface susceptibility or bulk dielectric function. We discuss in details the origin of the discrepancies and show that our approach allows to determine intrinsic properties of the bidimensional materials with the advantage that multilayer and monolayer systems are described in a same framework.