Multilayer C and BN δ‐Graphyne Sheets: An Exploration of Electronic and Optical Characteristics

Abstract

The structural, electronic, and optical characteristics of multilayer C δ‐graphyne and δ‐graphyne‐like BN sheets are discussed by first‐principles study. The calculations approved that the sheets are energetically favorable and thermally stable. The layers are held together by van der Waals forces. The mono‐ and tri‐layer C δ‐graphyne exhibit semimetallic behavior, while bi‐ and tetra‐layer C δ‐graphyne are semiconductors with negligible bandgap. All multilayer BN δ‐graphyne sheets are insulators with indirect bandgap. The bandgap increases with increasing number of layers. The optical behavior of the structures is anisotropic under electric fields polarized parallel and perpendicular to the sheets. The sheets exhibit high static dielectric constants, optical absorption, and optical conductivity. The electronic and optical characteristics of C and BN δ‐graphyne sheets promise their progress and application in the world of optoelectronics.

Comparative Study of δ-Graphdiyne and δ-Graphyne: Insights into Structural Stability and Electronic and Optical Properties

“…To determine the lattice constants of the sheets, the variations of the total energy, E sheet , as a function of the lattice constant, a = b , are shown in Figure . The minimum points of these curves specify that the lattice constant of δ-graphyne is 9.44 Å, in good agreement with previous studies. , The value of the lattice constant is found to be 13.95 Å for δ-graphdiyne. The configurations of δ-graphyne and δ-graphdiyne have both sp- and sp 2 -hybridized carbon atoms as illustrated in Figure .…”

“…Also, zero DOS at the Fermi energy indicates the presence of the Dirac cones. It is clear that, insensitive to the sheet size, δ-graphyne is a semimetal as expected from the prior studies. , Similar to δ-graphyne, δ-graphdiyne exhibits a semimetallic behavior. The charge carriers in the valence and conduction bands surrounding the Dirac points for δ-graphyne and δ-graphdiyne will behave as massless Dirac Fermions, like the cases for the well-known materials such as graphene, silicene, and germanene. − It is clear from pDOS that the linear dispersion of the valence and conduction bands at the Fermi level is mainly due to the p z orbital of the carbon atom.…”

“…It is found that the static reflective index of δ-graphdiyne (3.66) is close to that of δ-graphyne (3.73) and more than that of graphene (2.76) in the case of parallel polarization. For perpendicular polarization, the static reflective index is 1.04 for δ-graphdiyne close to δ-graphyne (1.07) and graphyne (1.1), and lesser than graphene (1.15), silicene (1.47), and germanene (1.51). ,, These large values in δ-graphdiyne and graphyne sheets indicate a high available concentration of free charge carriers.…”

“…Thus, the carbon atoms are covalently bound to each other. The δ-graphdiyne with a cohesive energy of −8.20 eV/atom is slightly less stable than δ-graphyne with a cohesive energy of −8.31 eV/atom. , The cohesive energies indicate that δ-graphyne and δ-graphdiyne are more stable than α- and β-graphyne sheets …”

“…It is shown that δ-graphyne is more stable than the well-known graphyne sheets, such as α- and β-graphyne. The electronic band structure of δ - graphyne can be characterized by the Dirac cones similar to graphene, α-, and β-graphyne sheets. , In the present work, a carbon monolayer named δ-graphdiyne is introduced and compared to δ - graphyne. Their structural, electronic, and optical properties are studied by density functional theory (DFT) calculations.…”