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.
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We thank R. Arita and N. Nagaosa for useful discussions and feedback and F. Bertran and P. Le Fèvre for ongoing technical support of the CASIOPEE beam line at SOLEIL. We gratefully acknowledge support from the CREST, JST (Nos JPMJCR16F1 and JPMJCR16F2), the Leverhulme Trust, the Engineering and Physical Sciences Research Council, UK (Grant Nos EP/M023427/1 and EP/I031014/1), the Royal Society, the Japan Society for Promotion of Science (Grant-in-Aid for Scientific Research (S); No. 24224009 and (B); No. 16H03847), the International Max-Planck Partnership for Measurement and Observation at the Quantum Limit, Thailand Research Fund and Suranaree University of Technology (Grant No. BRG5880010) and the Research Council of Norway through its Centres of Excellence funding scheme, project number 262633, QuSpin, and through the Fripro program, project number 250985 FunTopoMat. This work has been partly performed in the framework of the nanoscience foundry and fine analysis (NFFA-MIUR Italy, Progetti Internazionali) facility. B.-J. Y. was supported by the Institute for Basic Science in Korea (Grant No. IBS-R009-D1), Research Resettlement Fund for the new faculty of Seoul National University, and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 0426-20150011). O.J.C., L.B., J.M.R. and V.S. acknowledge EPSRC for PhD studentship support through grant Nos EP/K503162/1, EP/G03673X/1, EP/L505079/1 and EP/L015110/1. I.M. acknowledges PhD studentship support from the IMPRS for the Chemistry and Physics of Quantum Materials. We thank Diamond Light Source (via Proposal Nos SI9500, SI12469, SI13438 and SI14927) Elettra, SOLEIL, and Max-Lab synchrotrons for access to Beamlines I05, APE, CASSIOPEE, and i3, respectively, that contributed to the results presented here.
The authors declare no competing financial interests.
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Bahramy, M., Clark, O., Yang, B. et al. Ubiquitous formation of bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides. Nature Mater 17, 21–28 (2018). https://doi.org/10.1038/nmat5031
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