Local Probe Spectroscopy of Two-Dimensional van der Waals Heterostructures

A large family of materials, collectively known as "van der Waals materials", have attracted enormous research attention over the past decade following the realization that they could be isolated into individual crystalline monolayers, with charge carriers behaving effectively two-dimensionally. More recently, an even larger class of composite materials has been realized, made possible by combining the isolated atomic layers of different materials into "van der Waals heterostructures", which can exhibit electronic and optical behaviors not observed in the parent materials alone. This thesis describes efforts to characterize the atomic-scale structural and electronic properties of these van der Waals materials and heterostructures through scanning tunneling microscopy measurements.;The majority of this work addresses the properties of monolayer and few-layer graphene, whose charge carriers are described by massless and massive chiral Dirac Hamiltonians, respectively. In heterostructures with hexagonal boron nitride, an insulating isomorph of graphene, we observe electronic interference patterns between the two materials which depend on their relative rotation. As a result, replica Dirac cones are formed in the valence and conduction bands of graphene, with their energy tuned by the rotation. Further, we are able to dynamically drag the graphene lattice in these heterostructures, owing to an interaction between the scanning probe tip and the domain walls formed by the electronic interference pattern. Similar dragging is observed in domain walls of trilayer graphene, whose electronic properties are found to depend on the stacking configuration of the three layers.;Scanning tunneling spectroscopy provides a direct method for visualizing the scattering pathways of electrons in these materials. By analyzing the scattering, we can directly infer properties of the band structures and local environments of these heterostructures. In bilayer graphene, we map the electrically field-tunable band gap and extract electronic hopping parameters. In WSe 2, a semiconducting transition metal dichalcogenide, we observe spin and layer polarizations of the charge carriers, representing a coupling of the spin, valley and layer degrees of freedom.