Unremovable linked nodal structures in stacked bilayer graphene with Kekulé texture

Linking structure is a new concept characterizing topological semimetals, which indicates the interweaving of the gap closing nodes at the Fermi energy (E_F) with other nodes below E_F. As the number of linked nodes can be changed only via pair-creation or pair-annihilation, a linked node is more stable and robust than ordinary nodes without linking.

We propose a new type of a linked nodal structure between a nodal line (nodal surface) at E_F with another nodal line (nodal surface) below E_F in two-dimensional (three-dimensional) systems with two chiral symmetries and negligible spin-orbit coupling. Contrary to the cases of linked nodes reported previously, in our system, a double band inversion creates a pair of linked nodes carrying the same topological charges, thus the pair are unremovable via a Lifshiftz transition. A realistic tight binding model and effective theory are developed for such a linking structure, and also a class of candidate materials are predicted using density functional theory (DFT) calculations. Experimental aspect of the proposed theory and predicted compounds are also discussed.