Origins of Dirac cones and parity dependent electronic structures of α-graphyne derivatives and silagraphynes

Compared with graphene, graphyne and its derivatives possess more diversified atomic configurations and richer electronic structures including Dirac cones (DCs) and metallic features depending on the parity of the number of sp carbon atoms of graphynes. This report described conceptually the process of DC formation of α-graphyne within a tight-binding framework parameterized from density functional calculations. We propose a "triple coupling" mechanism elucidating the DC formation and some flat bands of α-graphynes where the couplings among the three sp carbon chain atoms are critical. The extension of this mechanism further explains the origins of DCs of silagraphynes and the parity dependent electronic structures of α-graphyne derivatives with extended sp carbon chains. Understanding these origins helps in tuning electronic properties in the design of C or C-Si based nanoelectronic devices.