Multidimensional analysis of excitonic spectra of monolayers of tungsten disulphide: Towards computer vision of physically distinct spatial domains of 2D materials

Despite monolayers holding great promise for a broad range of applications, the research around 2D materials suggests that proliferation of the potential devices and their fulfillment of real-life demands are still far from realization. Experimentally obtainable samples commonly experience a wide range of perturbations (ripples and wrinkles, point and line defects, grain boundaries, strain field, doping, water intercalation, oxidation, edge reconstructions) significantly deviating crystal structure from idealistic models. These perturbations, in general, can be entangled or occur in groups with each group forming a complex perturbation making the interpretations of observable physical properties and the disentanglement of simultaneously acting effects a highly non-trivial task even for an experienced researcher, and advanced characterisation methods are often desirable. Here we generalise statistical correlation analysis of excitonic spectra of monolayer WS$_2$, acquired by hyperspectral absorption and photoluminescence imaging, to a multidimensional case, and examine multidimensional correlations via unsupervised machine learning algorithms. We are able to distinguish between different sets of perturbations acting on the otherwise ideal crystal structure and reveal multiple heterogeneous regions with an unprecedented level of details. This approach can be applied to any multi-modal imaging data acquired from other 2D materials, and our study paves the way towards advanced, machine-aided, characterisation of monolayer matter.