Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekul\'{e} texture

TL;DR

This paper introduces a new type of linked nodal structure in topological semimetals, stabilized by crystalline symmetries, and proposes stacked bilayer graphene with Kekulé texture as a candidate material.

Contribution

It reveals a novel linked nodal structure stabilized by symmetries and develops models and DFT calculations to identify real materials hosting this structure.

Findings

Linked nodal structures are more stable due to topological linking.

A realistic tight-binding model and effective theory are constructed.

Stacked bilayer graphene with Kekulé texture can host these linked nodes.

Abstract

Linking structure is a new concept characterizing topological semimetals, which indicates the interweaving of 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. Here 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) spinless fermion systems with $\mathcal{IT}$ symmetry where $\mathcal{I}$ and $\mathcal{T}$ indicate inversion and time-reversal symmetries, respectively. Because of additional chiral and rotational symmetries, 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, which is clearly distinct from the cases of the linked nodes reported previously. A realistic tight binding model and effective theory are developed for such a linking structure. Also, using density functional theory calculations, we propose a class of materials, composed of stacked bilayer graphene with Kekul\'{e} texture, as a candidate system hosting the new type of the linked nodal structure.