Highly Controllable Quantum Dots in Moiré-of-Moiré Trilayer TMDs

We present theoretical studies on lattice relaxation and electronic structures in twisted trilayer transition metal dichalcogenides (TMD) with moiré-of-moiré patterns. By using the continuum model, we show that lattice relaxation leads to a patchwork of moiré-of-moiré domains, similar to twisted trilayer graphene. Electronic band calculations reveal the emergence of multiple flat bands near the Fermi energy, with electrons localized at the peaks of the intralayer potential of the TMD layer. We demonstrate that these flat bands, along with their real-space distribution, can be modulated by applying an electric field and lateral shifts of layers. This system serves as a candidate for highly controllable quantum dots, allowing manipulation through electric fields, lateral shifts, and hole doping. Our findings suggest that the alternate twist trilayer TMD not only possesses discrete multi-flat bands but also offers a platform for an effective Hubbard model with tunable lattice structures, characterized by the twist angles and electric field influences.