Nanoribbons are quasi one-dimensional materials which have completely different electronic properties, as compared to their two-dimensional parent materials. Low dimensionality leads to interesting electronic and magnetic properties which are result of the size and geometry of material, as well as constituent atoms. The interesting properties of nanoribbons help to tune the band gap on the basis of their widths, and edge passivating atoms. Recent developments have shown that it is possible to combine hybrid structures of graphene and hexagonal boron-nitride monolayer. Thus, boron-nitride-carbon (BNC) nanoribbons (BNCNRs) are hybrid structures composed of graphene nanoribbons (GNRs) and boron-nitride nanoribbons (BNNRs). SiC nanoribbons (SiCNRs) also emerged as promising materials because they have interesting electronic properties. We carried out first-principles many-body calculations for electronic and optical properties of hydrogen-passivated armchair SiCNRs (ASiCNRs), zigzag SiCNRs (ZSiCNRs), bare ASiCNRs, hydrogen-passivated armchiar BNCNRs (ABNCNRs), and zigag BNCNRs (ZBNCNRs) using density-functional theory and many-body approaches. Many-body effects are incorporated using the GW approximation and Bethe-salpeter equation (BSE) in order to calculate quasiparticle band gaps, and optical absorption spectra of SiCNRs and BNCNRs. From our calculations we conclude that hydrogen-passivated ASiCNRs are direct band gap semiconductors, and bare ASiCNRs undergo significant edge reconstruction, and become indirect band gap semiconductors. Self-energy corrections widened the band gaps, and excitonic effects modified optical absorption spectra dramatically for both the H-saturated and the bare ribbons. Our results predict that quasiparticle band gaps of hydrogen passivated and bare ASiCNRs are ~2 eV larger than their Kohn-Sham band gaps, due to the inclusion of many-body effects within the GW approximation. These large quasiparticle corrections to the band gaps suggest enhanced Coulomb correlation effects in reduced dimensions. Our BSE based calculations of the excitonic effects predict large excitonic binding energies in the range of 0.62-2.45 eV in optical absorption spectra of both types of ASiCNRs. We also studied the ZSiCNRs, with widths between 0.6 nm and 2.2 nm. We found that self-energy corrections transform nearly half-metallic ZSiCNRs with width larger than 1 nm, to semiconductors. For example, ZSiCNR with a width of 0.6 nm was found to have strongly bound excitons, with binding energy of 2.1 eV. We also computed the edge formation energy, and showed that ultra narrow ribbons are more stable when compared to larger ones. We also studied hydrogen-passivated ABNCNRs and ZBNCNRs which have an equal number of C-C and B-N bonds. We found that ABNCNRs are non-magnetic semiconductors, whose band gaps can be tuned between those of armchiar GNRs, and armchair BNNRs, based on the relative carbon composition. Similar to the case of SiCNRs, self-energy corrections widened the band gaps of ABNCNRs by up to 2 eV. Our calculations also suggest that ABNCNRs support strongly bound excitons, with binding energies in the range of 1.6–3.7 eV. We performed spin-polarized calculations for ZBNCNRs, and found that they exhibit an intrinsic half-metallic behavior that is completely dependent on the width of the ribbon, and relative C, and BN compositions. We also performed electronic structure calculations on partially hydrogen-passivated ABNCNRs and ZBNCNRs. We found that partial edge passivation in ABNCNRs allows possibllity of tunable band gaps, with ribbons exhibiting metallicity, and semiconducting behavior, while the same on ZBNCNR renders them metallic, semiconducting, or half-metallic. Thus, our results suggest that ASiCNRs and ABNCRs can be used in optoelectronic device applications, while ZBNCNRs and ZSiCNRs can be used in spintronic devices.

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