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Discovering a new route for creation and manipulation of quantum
quasiparticles in solids Considered as an inorganic analogue of graphene, transition metal dichalcogenides (TMD’s) are currently amongst the most intensively studied materials due to their rich electronic properties. An international collaboration led by the groups of Dr. M. S. Bahramy at the University of Tokyo and Dr. P. King at the St. Andrews University as well as Prof. T. Sasagawa at the Tokyo Institute of Technology and their colleagues from nine other institutions has established a general principle to create and control a variety of quantum quasiparticles in a group of TMD compounds. The research published online this week in the journal Nature Materials describes how these materials can inherently host different types of so-called bulk Dirac fermions and topological surface states. These findings offer a universal roadmap for design and control of topological materials, a new state of quantum matter with unusual physical properties.
Background
In the field of condensed matter physics, the relativistic motion of particles is described by a mathematical formula, known as Dirac equation. For fermions, particles like electron, the German physicist Herman Weyl predicted in 1929 that the absence of mass terms in the Dirac equation leads to a unique quantum state in which the fermions while still carrying a charge behave like a massless photon. In solids, this situation is manifested when two energy bands linearly cross each other. If the bands are spin-polarized, the resulting crossing is called a Weyl node and if they are spin-degenerate, it is referred to as a Dirac point. In the past few years, several Weyl and Dirac semi-metals have been theoretically predicted and/or experimentally discovered. However, these findings alone cannot give a clear vision for designing materials with such topological features. Moreover, the discovered Weyl nodes or Dirac points almost always happen to be the result of crossing between bands with different atomic or orbital characters, implying the need for specific stoichiometries for such phases.
Key concept
Bahramy and his colleagues have addressed this issue by proposing a general principle for creation and manipulation of Dirac fermions by using a single type of orbitals. This is enabled by an inherent geometrical aspect of some non-magnetic crystals with inversion symmetry, that is, rotational symmetry. The energy bands in such crystals are grouped into specific spin-degenerate branches with distinct symmetry properties along the rotational axis. Choosing
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an appropriate atomic arrangement, one can energetically tune these branches such that they cross each other along the rotational axis. Some of these crossings are protected against perturbations and, thus, form Dirac points. The others are gapped out by the spin-orbit interaction. Nonetheless, the latter still carry a non-trivial topology, manifested by a ladder of topological surface states (see figure, below). The resulting bulk Dirac points, appearing in pairs, are further categorized as Lorentz-variant (type I) or Lorentz-invariant (type II) depending on the relative slope of the corresponding bands. Regardless of their type, each pair is connected at the surfaces by two loops, known as Fermi arcs, as illustrated in the below figure.
Methodology and key findings
TMD’s appear to be an ideal example of topological materials, which naturally exhibit the above features even in their pristine state. In most of TMD’s, the unique arrangement of the atoms imposes strict rules on the characteristics of each energy band. Accordingly, any band crossing along the rotational axis results in distinct topological features. To show this, Dr. Bahramy and his colleagues have performed a series of electronic structure calculations for six TMD’s with different ingredients but all sharing the same rotational symmetry. For all these systems, the trend of crossing between the energy bands is shown to be the same. For the energy bands sharing the same symmetry characters, the crossing turns out to be unstable and thus gapped out by the spin-orbit interaction of electrons. In contrast, the crossing between the bands of different symmetry characters is found to be robust, thereby forming a double cone, also known as Dirac cone, with a tilted orientation. Remarkably, for the creation of such Dirac points, only the p orbitals of chalcogen atoms are needed. Moreover, in some cases like PdTe2, both type-I and type-II Dirac points can be seen simultaneously. “This is a remarkable finding. In no other known Dirac semimetal, the coexistence of these two phases has been reported. Each of these phases has its own topological features. Having them together in the same system enables us to search for emergent quantum phenomena that are not realizable in either of phases, separately,” says Dr. Bahramy.
The predicted results are confirmed by the state-of-art angle-resolved photoemission spectroscopy (ARPES) measurements, a powerful technique allowing the direct observation of the electronic structure of solids. Performed at the Diamond Light Source center in the UK, SOLEIL synchrotron facilities in France, Elettra Sincrotrone Trieste in Italy and MAX IV Laboratory in Sweden, the reported ARPES measurements also show very similar topological features in PdTe2 and other TMD’s. In agreement with theoretical results, the ARPES data also confirm that the gapped crossings carry a non-trivial topology manifested by spin-polarized surface states and surface resonances. Based on these findings, the authors have proposed a universal theoretical model, which successfully describes all possible topological phases, resulting from rotational
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symmetry in TMD’s. General principles have also been drawn from this model which can be served as a roadmap to create and control similar quantum quasiparticles in other materials.
Outlook
Transition metal dichalcogenides are best known for their unique electronic, spintronic and valleytronic properties. Knowing that they can inherently host such novel topological phases brings about new possibilities for realization of next-generation electronic devices with advanced functionalities. The principle underlying the formation of bulk Dirac cones and topological surface states proposed in this work is very general, and can be expected to occur across numerous materials systems. Moreover, demonstration of their existence across multiple TMD’s indicates that there is still significant opportunity to tailor the properties, locations, and nature of these states. "The number of ingredients you need to enable these features to arise in a material is very small, and each of them very common. This therefore drastically expands the range of possible materials in which you can expect to find these topological signatures," Mr. Calrk, one of the main authors of the paper, explains. This study thus opens routes to the rational design of topological materials.
Figure
An illustration of topological states in energy-momentum space of TMD’s. The central energy band shares the same symmetry characters with the upper band and thus there’s a gap between them. On the other hand, it is symmetrically different from the lower band and thus they cross each other at two points, labeled as Dirac points, along the rotational axis. The projection of these states onto the surface, parallel to the rotational axis (labeled as [100]) reveals a connection between the two Dirac points via a pair of loops, known as Fermi arcs. At the surface perpendicular to the rotational axis (labeled as [001]), topological surface states appear in the gap between the upper and central bands.
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Bibliographical reference "Ubiquitous Formation of Bulk Dirac Cones and Topological Surface States from a Single Orbital Manifold in Transition-metal Dichalcogenides" M.S. Bahramy, O.J. Clark, B.-J. Yang, J. Feng, L. Bawden, J. M. Riley, I. Markovic, 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, and P.D.C. King Nature Materials (published on November 27, 2017) DOI: 10.1038/NMAT5031 Financial supports The research was partly supported by Japan Science and Technology (JST) Agency via Core Research for Evolutional Science and Technology (CREST) program under grants JPMJCR16F1 (represented by Prof. Masashi Kawasaki) and JPMJCR16F2 (represented by Prof. Takao Sasagawa). Contact information Mohammad Saeed Bahramy Lecturer Quantum-Phase Electronics Center Department of Applied Physics, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656 Japan TEL&FAX: +81-03-5841-6840, Email: [email protected] Unit Leader Emergent Computational Physics Research Unit RIKEN Center for Emergent Matter Science 2-1 Hirosawa, Wako, Saitama 351-0198 Japan TEL: +81-48-462-1111 (EXT. 3164), Email: [email protected] Takao Sasagawa Associate Professor Laboratory for Materials and Structures Institute of Innovative Research, Tokyo Institute of Technology R3-37, 4259 Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8503, JAPAN TEL & FAX: +81-45-924-5366, Email: [email protected] Philip King Royal Society Research Fellow and Reader in Physics SUPA, School of Physics and Astronomy, University of St. Andrews St Andrews, Fife, KY16 9SS, United Kingdom Tel: +44 (0)1334 463067, E-mail: [email protected]
