Tuning nodal line semimetals in trilayered systems
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part of Springer Nature, 2019 https://doi.org/10.1140/epjst/e2019-800179-x
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Tuning nodal line semimetals in trilayered systems Filomena Forte1,2,a , Delia Guerra2 , Canio Noce1,2 , Wojciech Brzezicki3 , and Mario Cuoco1,2 1 2
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CNR-SPIN, UOS di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy Dipartimento di Fisica “E.R. Caianiello”, Universit` a degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy International Research Centre MagTop at Institute of Physics, Polish Academy of Sciences, Aleja Lotnikw 32/46, 02668 Warsaw, Poland Received 9 October 2018 / Received in final form 28 November 2018 Published online 3 July 2019 Abstract. We investigate two-dimensional trilayered quantum systems with multi-orbital conduction bands, by focusing on the role played by the layer degree of freedom in setting the character of nodal line semimetals. The layer index can label the electronic states where the electrons reside in the unit cell and can enforce symmetry constraints in the electronic structure by protecting bands crossing. We demonstrate that both the atomic spin–orbit coupling and the removal of local orbital degeneracy can lead to different types of electronic transitions with nodal lines that undergo a changeover from a loop structure enclosing the center of the Brillouin zone to pockets winding around multiple high symmetry points. We introduce and employ a criterion to find the nodal lines transitions. On the basis of a zero-dimensional topological invariant that, for a selected electronic and energy manifold, counts the number of bands below the Fermi level with a given layer inversion eigenvalue in high symmetry points of the Brillouin zone, one can determine the structure of the nodal loops and the ensuing topological transitions.
1 Introduction Recently, the theoretical prediction [1–4] and experimental achievement [5–7] of topological insulators due to strong spin–orbit coupling (SOC) have dramatically enriched the scenario of phases of matter which can be obtained by suitably designing quantum materials. Apart from topological insulators [8,9], there has been a significant expansion towards topologically protected gapless phases, e.g. metals and semimetals [10–18], thus boosting the discovery of novel materials [19–25] with non-trivial band crossing points in the momentum space as well as quantum materials that combine topological and conventional forms of ordering. On a general ground, topological semimetals [26] are materials where conduction and valence bands exhibit crossings in some points or lines in the Brillouin zone and the crossings can occur as protected by a
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The European Physical Journal Special Topics
certain symmetry of the system or by the presence of topological invariants. Among the available topological gapless states, the Dirac semimetals owe a particular interest, with massless Dirac fermions emerging as low-energy fundamental excitations. Since the Dir
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