Supercell models are proposed to investigate the properties of three types of heterostructures formed by two-dimensional (2D) materials grown on metal substrates, including (1) silicon (Si) thin films on a silver (Ag) substrate; (2) a single-layer hexagonal boron nitride (h-BN) on ruthenium (Ru) and copper (Cu) substrates; and (3) a stacked combination of lead (Pb) and Ag thin films. Coverage, orbital hybridization, and interface conditions are studied in order to tailor the electronic properties of these heterostructures. For the first system, results show that a Si coverage beyond 2.5 ML is needed for the emergence of the nearly linear energy-momentum relation. This relation is associated with the electronic states induced by the interaction between surface Si and Ag. For the second system, results demonstrate that the nitrogen (N) orbitals can hybridize with the underlying metal orbitals, and thus the regions of the h-BN monolayer with N situated on top of a metal atom will move closer to the substrate, leading to a corrugated h-BN layer. Calculated spatially-periodic modulations of the band profile and the local work function are in agreement with the experimental results. For the third system, results illustrate that the presence of the substrate alters the boundary conditions and thus can change the phase shifts of the quantum well states at the interface. The combination of Pb and Ag films creates a joint potential well that supports combined quantum well states. These findings suggest that in our studied systems, the interaction between the 2D materials and the substrates plays an important role in determining their electronic properties.
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