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.

Author information

Author notes

    • M. S. Bahramy
    •  & O. J. Clark

    These authors contributed equally to this work.


  1. Quantum-Phase Electronics Center and Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan

    • M. S. Bahramy
  2. RIKEN center for Emergent Matter Science (CEMS), Wako 351-0198, Japan

    • M. S. Bahramy
  3. SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, Fife KY16 9SS, UK

    • O. J. Clark
    • , J. Feng
    • , L. Bawden
    • , J. M. Riley
    • , I. Marković
    • , F. Mazzola
    • , V. Sunko
    • , D. Biswas
    •  & P. D. C. King
  4. Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea

    • B.-J. Yang
  5. Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea

    • B.-J. Yang
  6. Center for Theoretical Physics (CTP), Seoul National University, Seoul 08826, Korea

    • B.-J. Yang
  7. Suzhou Institute of Nano-Tech and Nano-Bionics (SINANO) CAS, 398 Ruoshi Road, SEID, SIP, Suzhou 215123, China

    • J. Feng
  8. Diamond Light Source, Harwell Campus, Didcot OX11 0DE, UK

    • J. M. Riley
    • , T. K. Kim
    •  & M. Hoesch
  9. Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany

    • I. Marković
    •  & V. Sunko
  10. Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

    • S. P. Cooil
    • , M. Jorge
    •  & J. W. Wells
  11. MAX IV Laboratory, Lund University, PO Box 118, 221 00 Lund, Sweden

    • M. Leandersson
    •  & T. Balasubramanian
  12. Istituto Officina dei Materiali (IOM)-CNR, Laboratorio TASC, in Area Science Park, S.S.14, Km 163.5, I-34149 Trieste, Italy

    • J. Fujii
    •  & I. Vobornik
  13. Synchrotron SOLEIL, CNRS-CEA, L’Orme des Merisiers, Saint-Aubin-BP48, 91192 Gif-sur-Yvette, France

    • J. E. Rault
  14. Laboratory for Materials and Structures, Tokyo Institute of Technology, Kanagawa 226-8503, Japan

    • K. Okawa
    • , M. Asakawa
    •  & T. Sasagawa
  15. School of Physics and Center of Excellence on Advanced Functional Materials, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand

    • T. Eknapakul
    •  & W. Meevasana
  16. ThEP, Commission of Higher Education, Bangkok 10400, Thailand

    • W. Meevasana


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M.S.B. and B.J.Y. performed the theoretical calculations. The experimental data were measured by O.J.C., J.Feng, L.B., J.M.R., I.M., F.M., V.S., D.B., S.P.C., M.J., J.W.W., T.E., W.M. and P.D.C.K, and analysed by O.J.C.; M.L., T.B., J.Fujii, I.V., J.E.R., T.K.K. and M.H. maintained the ARPES/spin-resolved ARPES end stations and provided experimental support. K.O., M.A. and T.S. synthesized the measured samples. P.D.C.K., O.J.C. and M.S.B. wrote the manuscript with input and discussion from co-authors. P.D.C.K. and M.S.B. were responsible for overall project planning and direction.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to M. S. Bahramy or P. D. C. King.

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