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Vertical Heterostructures between Transition-Metal Dichalcogenides -- A Theoretical Analysis of the NbS$_2$/WSe$_2$ junction

Low-dimensional metal-semiconductor vertical heterostructures (VH) are promising candidates in the search of electronic devices at the extreme limits of miniaturization. Within this line of research, here we present a theoretical/computational study of the NbS$_2$/WSe$_2$ metal-semiconductor vertical hetero-junction using density functional theory (DFT) and conductance simulations. We first construct atomistic models of the NbS$_2$/WSe$_2$ VH considering all the five possible stacking orientations at the interface, and we conduct DFT and quantum-mechanical (QM) scattering simulations to obtain information on band structure and transmission coefficients. We then carry out an analysis of the QM results in terms of electrostatic potential, fragment decomposition, and band alignment. The behavior of transmission expected from this analysis is in excellent agreement with, and thus fully rationalizes, the DFT results, and the peculiar double-peak profile of transmission. Finally, we use maximally localized Wannier functions, projected density of states (PDOS), and a simple analytic formula to predict and explain quantitatively the differences in transport in the case of epitaxial misorientation. Within the class of Transition-Metal Dichalcogenide systems, the NbS$_2$/WSe$_2$ vertical heterostructure exhibits a wide interval of finite transmission and a double-peak profile, features that could be exploited in applications.