Ubiquitous formation of type-I and type-II bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides

Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied properties. They range from metals and superconductorsto 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 and performed spin- and angle- resolved photoemission (ARPES) and density-functional theory calculations for 1T-PdTe2 where the p- and d-orbital bands are well separated in energy. ARPES measurements were performed at the I05 beamline of Diamond Light Source-UK, and CASSIOPEE beamline of Synchrotron SOLEIL-France and the APE beamline of Elettra Syncrotrone Trieste-Italy, along with the majority of the spin-resolved ARPES measurements. Additional spin-resolved measurements were obtained from the I3 beamline of MAX IV Laboratory-Sweden.
Our ARPES measurements (hν= 80 -132 eV, kx = ky = 0) reproduce the calculated out-of-plane dispersion, revealing the formation of bulk Dirac points (BDPs) and gapped crossings of the upper pz and pxy-derived states (Fig.1a). The corresponding bulk Dirac cones and topological surface states located within the inverted band gaps are clearly observed (Fig.1c) in our ARPES measurements (hν= 27 eV (24 eV for inset)) and (Fig.1d) supercell calculations (projected onto the first 2 unit cells) along the Γ-M direction. To definitively identify its topological nature, we perform spin-resolved ARPES measurements (Fig.1e, f). Measured spin-resolved energy distribution curves along the lines shown in (Fig1.c) reveal a clear helical spin texture of the two topological surface states (TSS1 & 2), with an up-down-down-up relative ordering, as well as an additional spin-polarised state above TSS1 which we label SS. These results demonstrate that the co-existence of type-I and type-II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances are explained with the protected band crossing by the trigonal crystal field and the opening of the inverted band gap, within a single p-orbital manifold which is split with the crystal field and spin-orbit coupling. 

Figure 1Chalcogen-derived topological ladder in PdTe2.(a) Orbitally-resolved bulk electronic structure of PdTe2, indicating dominantly chalcogen-derived orbital character for the states in the vicinity of the Fermi level. (b) The measured out-of-plane dispersion together with the calculated band structure. Measured (c) and calculated (d) in-plane dispersion. (e,f) Spin-resolved energy distribution curves along the lines shown in (c).

Measured ARPES spectra for 1T-PdSe2 and 2H-WSe2 revealed that our theoretical approach is not limited to 1T-PdTe2, but the same topological signatures persist even within the more well-studied, d-band dominated members of the TMD classification. Figure 2(a) shows how the resulting band (anti) crossings drive successive transitions from a trivial semimetal to a type-II Dirac state to a system supporting a type-II Dirac fermion and an inverted band gap as a function of the ratio between inter-layer hopping (t3 (within unit cell), t4 (without unit cell) ) and intra-layer hopping (t1). Ultimately, these can even co-exist with a type I Dirac cone for large inter-layer hopping.
The insights gained here open new opportunities for topological “materials by design". Already, we demonstrate their existence in six separate TMDs, opening routes to tune, and ultimately exploit, their topological physics.

Figure 1.  Interlayer hopping-controlled topological and Dirac phases. (a,b) Effective phase diagrams for a minimal 2-site p-orbital tight-binding model. (c) Example electronic structure calculations along Γ-A for the points indicated in (a) and (b).


This research was conducted by the following research team:

M. S. Bahramy1,2, O. J. Clark3, B.-J. Yang4,5,6, J. Feng3, L. Bawden3, J. M. Riley3,7, I. Markovi3,8, F. Mazzola3, V. Sunko3,8, D. Biswas3, S. P. Cooil9, M. Jorge9, J. W. Wells9, M. Leandersson10, T. Balasubramanian10, J. Fujii11, I. Vobornik11, J. Rault12, T. K. Kim7, M. Hoesch7, K. Okawa13, M. Asakawa13, T. Sasagawa13, T. Eknapakul14, W. Meevasana14,15, P. D. C. King3

Quantum-Phase Electronics Center and Department of Applied Physics,The University of Tokyo, Tokyo, Japan
2 RIKEN center for Emergent Matter Science, Wako, Japan
3 SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews, United Kingdom
4 Department of Physics and Astronomy, Seoul National University, Seoul, Korea
5 Center for Correlated Electron Systems, Institute for Basic Science, Seoul, Korea
6 Center for Theoretical Physics (CTP), Seoul National University, Seoul, Korea
7 Diamond Light Source, Harwell Campus, Didcot, United Kingdom
8 Max Planck Institute for Chemical Physics of Solids, Dresden, Germany
9 Department of Physics, Norwegian University of Science and Technology,  Trondheim, Norway
10 MAX IV Laboratory, Lund University, Lund, Sweden
11 Istituto Offcina dei Materiali (IOM)-CNR, Laboratorio TASC, Trieste, Italy
12 Synchrotron SOLEIL, CNRS-CEA, L'Orme des Merisiers, Saint-Aubin,Gif-sur-Yvette, France
13 Laboratory for Materials and Structures, Tokyo Institute of Technology, Kanagawa, Japan
14 School of Physics, Suranaree University of Technology, Nakhon Ratchasima, Thailand
15 NANOTEC-SUT Center of Excellence on Advanced Functional Nanomaterials, Suranaree University of Technology, Nakhon Ratchasima, Thailand

Contact person:

Jun Fujii, email: 



M. S. Bahramy, O. J. Clark, B.-J. Yang, J. Feng, L. Bawden, J. M. Riley, I. Markovi, F. Mazzola, V. Sunko, D. Biswas, 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, “Ubiquitous formation of type-I and type-II bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides”, Nature Materials 17, 21 (2018); DOI: 10.1038/nmat5031

Last Updated on Wednesday, 24 January 2018 16:49