Illuminating the electronic properties of WS$_2$ polytypism with electron microscopy

Tailoring the specific stacking sequences (polytypes) of layered materials represents a powerful strategy to identify and design novel physical properties. While nanostructures built upon transition-metal dichalcogenides (TMDs) with either the 2H or 3R crystalline phases have been routinely studied, our knowledge of those based on mixed 2H/3R polytypes is far more limited. Here we report on the characterization of mixed 2H/3R free-standing WS$_2$ nanostructures displaying a flower-like configuration by means of advanced transmission electron microscopy. We correlate their rich variety of shape-morphology combinations with relevant local electronic properties such as their edge, surface, and bulk plasmons. Electron energy-loss spectroscopy combined with machine learning reveals that the 2H/3R polytype displays an indirect band gap with $E_{\rm BG}=1.6^{+0.3}_{-0.2}~{\rm eV}$. Further, we identify the presence of energy-gain peaks in the EEL spectra characterized by a gain-to-loss ratio $I_G/I_L>1$. Such property could be exploited to develop novel cooling strategies for atomically thin TMD nanostructures and devices built upon them. Our results represent a stepping stone towards an improved understanding of TMDs nanostructures based on mixed crystalline phases.