Single- and few-layer two-dimensional (2D) materials (nanolayer materials) and heterostructures exhibit striking quasiparticle properties and many-body interaction effects that offer exciting hunting ground for new physics. Quantum confinement and symmetry breaking that accompany reduced dimensionality in nanolayer materials give rise to emergent surface states with unique properties such as topologically protected surface states and other exotic surface states. The emergence of unexpected and often spectacular physical phenomena arises from the spatial distribution and dynamics of charge carriers on the surface, and localized interaction with photons, defects and external fields that can affect the qualitative features of many-body systems. A direct spatial nanoscale investigation of these surface states and a detailed understanding of their interactions with other systems is the goal of this research.