First-principles calculations of the electron-hole interaction in the optical responses of the B x C y N z monolayers.

We present first-principles calculations of the electronic and optical properties of both BCN and B4CN3 monolayers. Both systems exhibit semiconducting behavior. While BCN is nonmagnetic, B4CN3 exhibits spin polarization accompanied by a finite magnetic moment of 0.315 µ B. To clarify their electronic characteristics, we analyze the charge-density distributions and charge-density differences for all chemical bonds, along with the van Hove singularities in the density of states. More importantly, we further examine the optical responses with and without electron-hole interactions by evaluating the imaginary part of the dielectric function, energy-loss spectrum, absorption coefficient, and reflectance. The oscillator strengths of individual BSE excitonic states are analyzed to identify dark and bright excitons in BCN and B4CN3 monolayers, whose exciton binding energies are estimated to be 0.69 eV and 0.67 eV, respectively. Overall, our findings provide fundamental insight into orbital hybridization in low-dimensional systems and suggest practical routes for designing new materials for electronic, spintronic, and optoelectronic applications.