Tuning nodal line semimetals in trilayered systems

TL;DR

This paper explores how layer degrees of freedom and spin-orbit coupling influence the formation and topological transitions of nodal line semimetals in trilayered quantum systems with multi-orbital conduction bands.

Contribution

It introduces a criterion based on a zero-dimensional topological invariant to identify and analyze nodal line transitions in trilayered systems.

Findings

Layer index enforces symmetry constraints protecting band crossings.

Spin-orbit coupling induces transitions between different nodal line structures.

Topological invariant effectively characterizes nodal line changes.

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.