Seeing Electrons in Two Dimensions: Optically Excited States in 2D Materials 
 
Layered van-der-Waals crystals can be thinned down to produce stable two-dimensional monolayers. The first widely studied material in this class was graphene, a single layer of carbon atoms, with its semi-metallic character. In addition, monolayers with insulating and semiconducting 2D materials have been identified, as have been materials with ferromagnetic, ferroelectric, and even superconducting properties. These monolayers can, moreover, be stacked in an arbitrary manner, thus allowing for the combination different classes of materials in precisely controlled heterostructures that exhibit new properties not present in the individual layers.

In this lecture, we will describe the how light interacts with such 2D layers and how optical spectroscopy can be used to reveal the properties of electrons in 2D materials. In the 2D semiconductors, optically excited electrons and holes bind together as atom-like excitonic excited states. These states exhibit features that differ both from the excited states of isolated atoms and from excited states of three-dimensional crystals. The possibility to tune and modify the excited states by electric fields, strain, dielectric environment, and adjacent 2D materials will be discussed. Such studies provide fundamental understanding of physics in reduced dimensional systems and also reveal potential applications of 2D semiconductors in optoelectronics and quantum information science.