Electronic properties of graphyne-$N$ monolayer and its multilayer: even-odd effect and topological nodal line semimetalic phases

TL;DR

This study reveals an even-odd effect in the electronic structure of graphyne-$N$ monolayers and multilayers, showing topological nodal line semimetal phases for even-$N$ and trivial phases for odd-$N$, with pressure inducing phase transitions.

Contribution

It introduces the even-odd dependence of band structures in graphyne-$N$ and identifies topological nodal line semimetal phases in multilayers, expanding understanding of carbon allotropes' electronic properties.

Findings

Even-$N$ graphyne monolayers have doubly-degenerate bands near the Fermi level.

ABC multilayers of even-$N$ exhibit nodal-line semimetal phases with non-trivial topology.

External pressure can induce a topological phase transition from trivial to nodal line semimetal.

Abstract

We study the electronic structure and topological properties of monolayer and ABC-stacked multilayer of graphyne-$N$, which are a family of planar carbon sheets consisting of $sp$ and $sp_2$-bonding. By using the density-functional theory and the effective continuum model, we find a striking even-odd effect in the dependence of the band structure on $N$ (the number of carbon-carbon triple bonds between neighboring benzene rings). Specifically, even-$N$ graphyne monolayer has doubly-degenerate conduction and valence bands near the Fermi energy, and in its ABC multilayer, the band inversion of the doubly-degenerate bands leads to a nodal-line semimetal phase with non-trivial $\mathbb{Z}_2$ monopole charge. In contrast, odd-$N$ monolayer has singly-degenerate bands in separate valleys, and its ABC multilayer can have only $\mathbb{Z}_2$-trivial nodal lines. ABC graphynes with larger $N$ tend to be trivial insulators because of smaller interlayer coupling, while the external pressure induces a topological phase transition from the trivial phase to the nodal line semimetal phase.