Optical detection of the susceptibility tensor in two-dimensional crystals

Zhemi Xu,Michele Merano,Nicola Galvanetto,Pengfei Yang,Luzhao Sun,Zhongfan Liu,Yanfeng Zhang,Joshua D Elliott,Luca Dell’Anna,Davide Ferraro,Margherita Marsili,Yuechen Wang,Alessandro Martucci,Paolo Umari,Annamaria Zaltron

doi:10.1038/s42005-021-00711-3

Abstract

The out-of-plane optical constants of monolayer two-dimensional materials have proven to be experimentally elusive. Owing to their reduced dimensionality, optical measurements have limited sensitivity to these properties which are hidden by the optical response of the substrate. Therefore, there remains an absence of scientific consensus on how to correctly model these crystals. Here we perform an experiment on the optical response of a single-layer two-dimensional crystal that addresses these problems. We successfully remove the substrate contribution to its optical response by a step deposition of a monolayer crystal inside a thick polydimethylsiloxane prism. This allows for a reliable determination of both the in-plane and the out-of-plane components of its surface susceptibility tensor. Our results prescribe one clear theoretical model for these crystals. This precise characterization of their optical properties will be relevant to future progresses in photonics and optoelectronics with two-dimensional materials.

Highlights

The out-of-plane optical constants of monolayer two-dimensional materials have proven to be experimentally elusive
If the first ellipsometric data for graphene were fitted using a uniaxial thin film model[8], the subsequent analysis concluded that ellipsometry is only sensitive to the in-plane optical constants[1]
While the reflection coefficients for the anisotropic slab model are reported in ref. 21, it is much more difficult to find in the literature a complete and correct generalization of the surface current model to include the orthogonal polarization

Summary

Introduction

The out-of-plane optical constants of monolayer two-dimensional materials have proven to be experimentally elusive. We expect that the optical spectra of single-layer, two-dimensional (2D) crystals show out-of-plane anisotropy. Optical contrast measurements, used to detect single and multiple layers of a 2D crystal, are analyzed by choosing an isotropic thin film[5,7,10].

Results

Conclusion