M. S. Bahramy , O. J. Clark , B. -J. Yang , J. Feng , L. Bawden , J. M. Riley , I. Marković , F. Mazzola , V. Sunko , S. P. Cooil , M. Jorge , J. W. Wells , M. Leandersson , T. Balasubramanian , J. Fujii , I. Vobornik , J. Rault , T. K. Kim , M. Hoesch , K. Okawa , M. Asakawa , T. Sasagawa , T. Eknapakul , W. Meevasana , P. D. C. King
Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied properties. They range from metals and superconductors to strongly spin-orbit-coupled semiconductors and charge-density-wave systems, with their single-layer variants one of the most prominent current examples of two-dimensional materials beyond graphene. Their varied ground states largely depend on the transition metal d-electron-derived electronic states, on which the vast majority of attention has been concentrated to date. Here, we focus on the chalcogen-derived states. From density-functional theory calculations together with spin- and angle- resolved photoemission, we find that these generically host type-II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. We demonstrate how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across a large number of compounds. Already, we demonstrate their existence in six separate TMDs, opening routes to tune, and ultimately exploit, their topological physics.