Origin of Moiré Potentials in WS$_2$/WSe$_2$ Heterobilayers: Contributions from Lattice Reconstruction and Interlayer Charge Transfer

Moiré 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 moiré 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 moiré potentials in both R-type and H-type moiré patterns formed in WS$_2$/WSe$_2$ heterobilayers. We show that both lattice reconstruction and interlayer charge transfer contribute significantly to the formation of moiré 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 moiré and 40 meV for an H-type moiré. Taking into account both effects from lattice reconstruction and interlayer charge transfer, the formation of moiré potential is well understood for both R-type and H-type moirés. This trapping potential localizes the wavefunctions of conduction and valence bands around the same moiré site for an R-type moiré, while around different moiré site for an H-type one.

💡 Research Summary

This paper provides a comprehensive theoretical investigation of the origin of moiré potentials in WS₂/WSe₂ heterobilayers, focusing on both R‑type (0° twist) and H‑type (60° twist) configurations. The authors first perform large‑scale structural relaxations using classical force‑field simulations (LAMMPS) to capture the strong lattice reconstruction that occurs in these systems. In the R‑type case the low‑energy Rₓₕ stacking expands while the high‑energy Rₕₕ region contracts; in the H‑type case the Hₕₕ region expands at the expense of Hₘₕ. Both in‑plane strain (up to ~1 %) and out‑of‑plane corrugation (up to 2 Å) are observed, leading to a non‑uniform interlayer distance across the ~8 nm moiré period.

To connect structural changes with electronic properties, density‑functional theory (DFT) calculations are carried out on the relaxed structures. The band alignment is type‑I: the conduction‑band minimum resides in WS₂ (predominantly d_{z²}) and the valence‑band maximum in WSe₂ (predominantly d_{x²‑y²} and d_{xy}). Mini‑band calculations reveal a series of nearly flat bands near both band edges; the conduction miniband is flatter, indicating stronger confinement. Real‑space wave‑function plots show that in the R‑type moiré both electron and hole states are localized around the same high‑symmetry site (Rₘₕ), whereas in the H‑type they localize on different sites (electron at Hₕₕ, hole at Hₓₕ). This spatial separation explains recent experimental observations of inter‑cell moiré excitons with large in‑plane quadrupole moments.

The authors then dissect the contributions to the moiré potential. First, lattice reconstruction induces a local strain field. By applying the same strain to isolated monolayers, they find that a 1 % strain shifts the WS₂ conduction‑band edge by ~200 meV and the WSe₂ valence‑band edge by ~20 meV. Second, the non‑centrosymmetric deformation generates a piezoelectric potential that adds 40–90 meV depending on stacking and carrier type. Third, interlayer charge transfer creates an intrinsic electric field; DFT charge‑density analysis yields a built‑in potential of ~80 meV for the R‑type and ~40 meV for the H‑type moiré.

Summing these three mechanisms reproduces the full energy modulation observed in the DFT miniband spectra. In the R‑type moiré the combined effect yields a deep, symmetric potential well that traps both electrons and holes at the same site. In the H‑type moiré the combined effect produces an asymmetric landscape, leading to electron‑hole separation across the moiré unit cell. The quantitative agreement between the model and the first‑principles results validates the picture that strain‑induced band‑edge shifts, piezoelectric potentials, and charge‑transfer‑induced fields are the dominant, mutually reinforcing sources of moiré potentials in WS₂/WSe₂ heterostructures.

Overall, the work clarifies why WS₂/WSe₂ heterobilayers exhibit strong moiré confinement and provides design rules for engineering moiré potentials in other transition‑metal dichalcogenide heterostructures. By tuning lattice mismatch, twist angle, and dielectric environment, one can tailor the relative contributions of strain, piezoelectricity, and charge transfer to achieve desired flat‑band conditions, opening pathways toward controllable strongly correlated phases such as moiré Mott insulators, Wigner crystals, and exotic excitonic condensates.