Since the discovery of graphene in 2004, there has been a tremendous effort in materials science, physics, and chemistry to isolate and research the properties of other two-dimensional compounds. From a historical view, these pursuits and interests in these materials may seem frivolous, as the entire field of nanomaterials has moved from zero-dimensional quantum dots, to one-dimensional carbon nanotubes, to present day two-dimensional materials. However, the uniform and large scale growth of these materials is definitely a factor which has contributed to this field's longevity in research and driven interest in future device integration. In addition, the dangling bond free surface and chemical stability has played an important role in the fabrication of such devices and observation of unique physical and chemical phenomena.
In particular, the lack of bonding in the out-of-plane direction means that these bulk crystals are only held together by van der Waals forces. Thus, the material's layer geometry has a significant effect on the van der Waals crystal's observable properties. We demonstrate how the layer stacking geometry can significantly alter the nonlinear optical properties of the crystal, as shown with second harmonic generation. Furthermore, these two-dimensional crystals allows for a unique opportunity to artificially create nanomaterials composed of distinct crystals, so-called van der Waals heterostructures. These heterostructures may be assembled using chemical means, or via manual transfer, both of which are extensively covered in this thesis. Chemically assembled heterostructures of single layer graphene and the transition metal dichalcogenide molybdenum disulfide form all-two-dimensional transistors, capable of demonstrating logic. Manually transferring exfoliated crystals can lead to both the demonstration of devices, as well as the observation of new physical phenomena, such as the Coulomb drag of transition metal dichalcogenides.