  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.
