Optical modeling of single and multilayer two-dimensional materials and heterostructures

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 bidimensional 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 detail 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.