Origin of Moir\'{e} Potentials in WS$_2$/WSe$_2$ Heterobilayers: Contributions from Lattice Reconstruction and Interlayer Charge Transfer

Moir\'{e} superlattices formed in WS$_2$/WSe$_2$ heterobilayers have emerged as an exciting platform to explore the quantum many-body physics. The key mechanism is the introduction of moir\'{e} potentials for the band-edge carriers induced by the lateral modulation of interlayer interactions. This trapping potential results in the formation of flat bands, which enhances the strong correlation effect. However, a full understanding of the origin of this intriguing potential remains elusive. In this paper, we present a comprehensive investigation of the origin of moir\'{e} potentials in both R-type and H-type moir\'{e} patterns formed in WS$_2$/WSe$_2$ heterobilayers. We show that both lattice reconstruction and interlayer charge transfer contribute significantly to the formation of moir\'{e} potentials. In particular, the lattice reconstruction induces a nonuniform local strain, which creates an energy modulation of 200 meV for the conduction band-edge state located at WS$_2$ layer and 20 meV for the valence band-edge state located at WSe$_2$ layer. In addition, the lattice reconstruction also introduces a piezopotential energy, whose amplitude ranges from 40 meV to 90 meV depending on the stacking and band-edge carrier. The interlayer charge transfer induces a built-in electric field, resulting in an energy modulation of 80 meV for an R-type moir\'{e} and 40 meV for an H-type moir\'{e}. Taking into account both effects from lattice reconstruction and interlayer charge transfer, the formation of moir\'{e} potential is well understood for both R-type and H-type moir\'{e}s. This trapping potential localizes the wavefunctions of conduction and valence bands around the same moir\'{e} site for an R-type moir\'{e}, while around different moir\'{e} site for an H-type one.