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We model monolayer graphene-like materials with BC$_6$N stoichiometry wherethe bonding between the B and the N atoms plays an important role for theirphysical and chemical properties. Two types of BC$_6$N are found based on theBN bonds: In the presence of BN bonds, an even number of $\pi$-bonds emergesindicating an aromatic structure and a large direct bandgap appears, while inthe absence of BN bonds, an anti-aromatic structure with an odd-number of$\pi$-bonds is found resulting a direct small bandgap. The stress-strain curvesshows high elastic moduli and tensile strength of the structures with BN-bonds,compared to structures without BN-bonds. Self-consistent field calculationsdemonstrate that BC$_6$N with BN-bonds is energetically more stable thanstructures without BN-bonds due to a strong binding energy between the B andthe N atoms, while their phonon dispersion displays that BC$_6$N withoutBN-bonds has more dynamical stability. Furthermore, all the BC$_6$N structuresconsidered show a large absorption of electromagnetic radiation withpolarization parallel to the monolayers in the visible range. Finer detail ofthe absorption depend on the actual structures of the layers. A higherelectronic thermal conductivity and specific heat are seen in BC$_6$N systemscaused by hot carrier--assisted charge transport. This opens up a possibleoptimization for bolometric applications of graphene based material devices.

Modeling electronic, mechanical, optical and thermal properties of graphene-like BC$_6$N materials: Role of prominent BN-bonds