Precise Effective Continuum Model in Moiré Superlattice systems

The moiré superlattice system provides an excellent platform for studying many interesting phenomena. However, formulating an effective low-energy model as a starting point is not a straightforward task, especially when considering twisted transition metal dichalcogenide (tTMD) systems. Merely treating the moiré potential as a series of parameters does not help us understand the behavior of the system. In this work, we theoretically investigate the lattice relaxation effects in twisted bilayer graphene (TBG) and tTMD systems, as well as the electronic effective continuum model that considers these lattice relaxation effects.

We find that lattice relaxation effects significantly influence the low-energy electronic structure of the system. Therefore, we constructed an electronic continuum model that fully accounts for lattice relaxation effects. For TBG, the electronic band structure obtained by solving the effective continuum model is almost identical to that derived using a tight-binding model. For tTMD, we fitted a set of parameters that describe the effect of microscopic hopping, which are independent of the twist angle, enabling us to accurately reproduce the tTMD electronic band structure obtained from first-principles calculations. In our tTMD continuum model, each term has a clear physical interpretation, allowing us to gain a more precise and in-depth understanding of the tTMD system. Our model thus lays a foundation for further research into correlated states in tTMD systems.