Designing All Graphdiyne Materials as Graphene Derivatives: Topologically Driven Modulation of Electronic Properties

Designing new 2D
systems with tunable properties is an important
subject for science and technology. Starting from graphene, we developed
an algorithm to systematically generate 2D carbon crystals belonging
to the family of graphdiynes (GDYs) and having different structures
and sp/sp2 carbon ratios. We analyze how structural and
topological effects can tune the relative stability and the electronic
behavior, to propose a rationale for the development of new systems
with tailored properties. A total of 26 structures have been generated,
including the already known polymorphs such as α-, β-,
and γ-GDY. Periodic density functional theory calculations have
been employed to optimize the 2D crystal structures and to compute
the total energy, the band structure, and the density of states. Relative
energies with respect to graphene have been found to increase when
the values of the carbon sp/sp2 ratio increase, following
however different trends based on the peculiar topologies present
in the crystals. These topologies also influence the band structure,
giving rise to semiconductors with a finite band gap, zero-gap semiconductors
displaying Dirac cones, or metallic systems. The different trends
allow identifying some topological effects as possible guidelines
in the design of new 2D carbon materials beyond graphene.