Evolution of band topology in twisted MoTe₂ and WSe₂ driven by polarization

Motivated by recent observations of opposite Chern numbers in twisted MoTe₂ and WSe₂ at integer filling factor, we use large-scale density-functional-theory (DFT) calculations to investigate the twist-angle dependence of band topology. We show that the in-plane lattice relaxations at the moiré scale lead to redistribution of polarization charge, a key factor not captured by local-stacking approximations. This reshapes the moiré potential, and results in the evolution of Chern numbers as a function of twist angles in both MoTe₂ and WSe₂. Our conclusions are corroborated by the analysis of electrostatic potential, which shows rich patterns governed by the polarization charge. We further demonstrate that the moiré wavefunction profile shifts across different stacking regions as a function of twist angle. Our results not only unveil the origin of band topology in twisted transition metal dichalcogenides, but also provide a basis to study intertwined correlation and topology with quantitative accuracy.