Tight-binding theory of spin-orbit coupling in graphynes

Abstract

Graphynes represent an emerging family of two-dimensional carbon allotropes that recently attracted much interest due to the tunability of the Dirac cones in the band structure. We explore the effects of spin-orbit couplings, both Rashba and intrinsic ones, in these systems. First, we develop a general method to address spin-orbit couplings within tight-binding theory. We then apply this method to describe the effects of spin-orbit couplings in α, β, and γ-graphyne. We show how spin-orbit couplings can lead to various effects related to both topological and non-topological properties of their band structures. In α-graphyne, as in graphene, the Rashba spin-orbit coupling splits each Dirac cone into four, whereas the intrinsic spin-orbit coupling opens a topological gap. In β-graphyne, intrinsic spin- orbit coupling yields high- and tunable Chern-number bands, which may host both topological and Chern insulators, in the presence and absence of time-reversal symmetry, respectively. On the other hand, Rashba spin-orbit coupling can be used to control the position and the number of Dirac cones in the Brillouin zone. Finally, the Rashba spin-orbit coupling can close the band gap in γ-graphyne.