What Can ABACUS Do Too? | ABACUS + DeepH + KPROJ: Unraveling the Electronic Structure of MoSe₂/WSe₂ Moiré Lattices
Recently, the research group led by Mingxing Chen from the College of Physics and Electronic Science at Hunan Normal University investigated the evolution of flat bands in the MoSe₂/WSe₂ moiré lattices of transition metal dichalcogenides using deep learning potential and Hamiltonian models. In this study, they employed the domestic first-principles software ABACUS, which is based on the linear combination of atomic orbitals (LCAO) basis set, to prepare machine learning datasets. Subsequently, they used DeepH, based on E3 equivariant graph neural networks, to train machine learning models for predicting the moiré lattice Hamiltonian. Diagonalizing the machine learning Hamiltonian yielded the electronic structure of the moiré system. Thereafter, they utilized the self-developed band unfolding program KPROJ to project the wavefunctions of the moiré supercell onto the k-points of the primitive cell and obtained the unfolded band structure, which was used to study the influence of the twist angle on the band structure of transition metal dichalcogenides. This work revealed that the flat bands originating from the valence band edge can stem from the Γ and K valleys. When the H-stacked MoSe₂/WSe₂ moiré lattice has a twist angle of 3.89˚ and spin-orbit coupling (SOC) is not considered, a flat band with a bandwidth of approximately 5 meV appears below the valence band edge at the K point. Subsequently, as the twist angle decreases, this flat band rapidly shifts upward and becomes approximately 20 meV higher than the valence band at the K point. When the twist angle further decreases to 1.7˚, multiple flat bands emerge. The research found that spin-orbit coupling leads to a large spin splitting, comparable to that in the untwisted system (approximately 0.45 eV), and is almost independent of twisting and stacking. Therefore, in the presence of spin-orbit coupling, the flat band in the K valley remains at the top of the valence band. The band unfolding results indicate that the flat bands formed by the Γ valley and the K valley exhibit distinct responses to the twist angle. The Γ valley flat band is highly sensitive to the interlayer coupling and thus rapidly shifts upward as the twist angle decreases. Conversely, the K valley flat band has a weaker dependence on the interlayer coupling and is primarily affected by structural reconstruction. Hence, a relatively small angle (2.13˚) is required to generate the K valley flat band. As the twist angle decreases, this flat band transforms from a honeycomb lattice to a triangular lattice. The relevant research, titled "Evolution of flat bands in MoSe₂/WSe₂ moiré lattices: A study combining machine learning and band unfolding methods", was published in Physical Review B [Phys. Rev. B 110, 235410 (2024)]. Doctoral students Shengguo Yang and Jiaxin Chen are the first and second authors respectively, and Mingxing Chen is the corresponding author.