Origins of Dirac cone formation in AB₃ and A₃B (A, B = C, Si, and Ge) binary monolayers

Compared to the pure two-dimensional (2D) graphene and silicene, the binary 2D system silagraphenes, consisting of both C and Si atoms, possess more diverse electronic structures depending on their various chemical stoichiometry and arrangement pattern of binary components. By performing calculations with both density functional theory and a Tight-binding model, we elucidated the formation of Dirac cone (DC) band structures in SiC₃ and Si₃C as well as their analogous binary monolayers including SiGe₃, Si₃Ge, GeC₃, and Ge₃C. A "ring coupling" mechanism, referring to the couplings among the six ring atoms, was proposed to explain the origin of DCs in AB₃ and A₃B binary systems, based on which we discussed the methods tuning the SiC₃ systems into self-doped systems. The first-principles quantum transport calculations by non-equilibrium Green's function method combined with density functional theory showed that the electron conductance of SiC₃ and Si₃C lie between those of graphene and silicene, proportional to the carbon concentrations. Understanding the DC formation mechanism and electronic properties sheds light onto the design principles for novel Fermi Dirac systems used in nanoelectronic devices.