An Atlas of Chirality-Dependent Electronic Structures of MoS ₂ Nanotubes from Deep Learning

Transition-metal dichalcogenide (TMD) nanotubes represent an emerging class of one-dimensional (1D) materials. However, our understanding of their chirality-dependent electronic properties has been limited. Here, we develop an integrated machine learning (ML) framework, combining ML interatomic potential with deep-learning density functional theory, to enable accurate and efficient prediction of the electronic structures of MoS₂ nanotubes across the entire chirality space. We construct a comprehensive atlas of their bandgaps, carrier effective masses, and direct-versus-indirect bandgap classification. We find that the bandgaps are primarily determined by tube diameter, whereas the carrier effective masses show a significant, nontrivial dependence on both tube curvature and chirality. In particular, a sharp increase in hole effective mass occurs for tube diameters below 62 Å, attributed to a universal strain-induced transition in the valence band maximum. These results provide significant insights into the properties of 1D TMD systems.