Eur. Phys. J. Special Topics 228, 643–657 (2019)
https://doi.org/10.1140/epjst/e2019-800179-x

Regular Article

Tuning nodal line semimetals in trilayered systems

¹ CNR-SPIN, UOS di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy
² Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy
³ International Research Centre MagTop at Institute of Physics, Polish Academy of Sciences, Aleja Lotnikw 32/46, 02668 Warsaw, Poland

^a e-mail: forte@sa.infn.it

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.