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Bahramy, M. ,S.,Clark, O. ,J.,Yang, B.-J.,Feng, J.,Bawden, L.,Riley, J. ,M.,Marković,, I.,Mazzola, F.,Sunko, V.,Biswas, D.,Cooil, S. ,P.,Jorge, M.,Wells, J. ,W.,Leandersson, M Nature Publishing Group, a division of Macmillan P 2018 NATURE MATERIALS Vol.17 No.1
Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied bulk properties, while their single-layer variants have become one of the most prominent examples of two-dimensional materials beyond graphene. Their disparate ground states largely depend on 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 a co-existence of type-I and 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.