| Summary: | We study the spatial modulation of the wave function in bilayer and trilayer graphene systems originating from two underlying mechanisms: quantum interference phenomena (QIP) and quantum confinement. We also take a bottom-up approach to tailoring surface potential distributions at the atomic scale to influence/control electron behaviour, by utilising the interaction between graphene layers and nanostructured, atomically flat insulating ionic surfaces. Quantum interference phenomena were explored at bilayer-trilayer armchair interfaces in multilayer graphene with various stacking orders by using scanning tunnelling microscopy and with support from theoretical simulations. Effects of various types of edges, which terminate the stacks abruptly or appear at lateral interfaces within the multistack, were revealed and correlated with scattering mechanisms, while a taxonomy of interference patterns was established based on stacking order. The effect of extra sources of scattering was also studied to understand the origin of the well-known (√3×√3)퐑퐑 30° superstructure in graphene systems, and a new explanation was proposed based on decomposing defects into armchair contours, able to provide multiple sources of scattering. The energy dependency of the (√3×√3)퐑퐑 30° superstructure and its motifs was quantitatively explored in bilayer graphene. Finally, bilayer and trilayer graphene were overlaid on atomically flat insulating surfaces decorated with nanostructures such as step edges and closed contours, and able to induce sizeable local electrostatic potential distribution within the graphene overlayers. A well-defined, rectangular subsurface potential distribution, akin to a nanoscale quantum box applied to a physically unconfined graphene overlayer, produced state localization in the local density of states of a trilayer, while resonances were also observed in bilayer graphene around irregular subsurface features within the ionic substrate. A 1D periodic superstructure also emerged from the interaction of bilayer graphene with large area flat regions of these ionic substrates with square symmetry.
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