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Novel bonding patterns and optoelectronic properties of the two-dimensional Si$_x$C$_y$ monolayers

The search of new two-dimensional (2D) materials with novel optical and electronic properties is always desirable for material development. Here, we report a comprehensive theoretical prediction of 2D SiC compounds with different stoichiometries from C-rich to Si-rich. Besides the previously known hexagonal SiC sheet, we identified two types of hitherto-unknown structural motifs with distinctive bonding features. The first type of 2D SiC monolayer, including t-SiC and t-Si$_2$C sheet, can be described by tetragonal lattice. Among them,t-SiC monolayer sheet is featured by each carbon atom binds with four neighboring silicon atoms in almost the same plane, constituting a quasi-planar four-coordinated rectangular moiety. More interestingly, our calculations demonstrate that this structure exhibits a strain-dependent insulator-semimetal transition, suggesting promising applications in strain-dependent optoelectronic sensors. The second type of 2D SiC sheet is featured by silagraphyne with acetylenic linkages(-C$\equiv$C-). Silagraphyne shows both high pore sizes and Poisson's ratio. These properties make them a potentially important material for applications in separation membranes and catalysis. Moreover, one of the proposed structures, $γ$-silagraphyne, is a direct-band-gap semiconductor with a bandgap of 0.89 eV, which has a strong absorption peak in the visible-light region, giving a promising application in ultra-thin transistors, optical sensor devices and solar cell devices.