Piecewise Hamiltonian construction of a metal (NbS₂)/semiconductor(WSe₂) two-dimensional (2D) hybrid heterojunction.

Density-Functional Theory studies of periodic systems can be greatly accelerated by projecting the Kohn-Sham Hamiltonian onto a limited basis set, as in the Tight-Binding (TB) and the Wannier approach to localized molecular orbitals. While the implementation of TB/Wannier approach is straightforward for systems composed of unit cells, the extension to complex, multi-component systems presents issues related to the homogeneous description of the different pieces and their interaction. Here we propose a simple protocol to decompose a system into fragments and re-build the Hamiltonian of the complete system in a piece-wise manner in terms of Hamiltonians of the separate fragments. A seamless junction between two different pieces is achieved by assuming buffer overlap regions between each pair of fragments and calculating the off-diagonal terms of the Hamiltonian by projecting the Wannier orbitals at the border of one fragment onto those of the neighboring module. We validate the method by applying it to a monolayer-thick lateral heterostructure joining two different transition metal dichalcogenides as a paradigmatic example of a metal (NbS₂)/semiconductor(WSe₂) hybrid heterojunction, finding a good agreement between exact and approximate Hamiltonians.