Electronic and optical properties of self-similar B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg" display="inline" id="d1e470"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> </mml:math> N <mm

This study employs first-principles calculations based on Density Functional Theory (DFT) to investigate the electronic and structural properties of boron-carbon-nitrogen (BCN) monolayers exhibiting quasi-periodic order within the unit cell, specifically following a Fibonacci-like sequence. To quantify the degree of disorder in these quasi-periodic BCN systems, we introduce a comparative metric against fully random BCN configurations. The analysis reveals a linear correlation between the degree of disorder and the electronic band width, indicating that increasing disorder enhances electron localization, with boron and nitrogen atoms acting as dopants within the graphene-like lattice. Furthermore, using a simplified tight-binding bond model, we extend the study to large-scale systems. Our results show that both the band gap and the degree of disorder become size-independent for Fibonacci BCN monolayers containing more than 288 atoms, a behavior attributed to the intrinsic self-similarity of quasi-periodic structures. Owing to electron localization, prominent peaks associated with electronic transitions between flat valence and conduction bands emerge in the absorbance spectra of large Fibonacci BCN systems. • Quasi-periodic BCN monolayers following a Fibonacci sequence are investigated. • A Pearson correlation metric quantifies disorder relative to random BCN systems. • Disorder degree linearly correlates with electronic band width and localization. • Band gap becomes size-independent for superlattices exceeding 288 atoms. • Optical spectra reveal distinct peaks from transitions between flat bands.