Correlation of Dirac ordering with optical activity in AlB2-type Dirac MBenes

Abstract Using first-principles calculations, this study systematically investigates the electronic properties and optical activity of AlB$_2$-type Dirac MBenes alongwith their correlations. Insights from phonon-spectral calculations and \textit{ab-initio} molecular dynamics simulations substantiates the thermally and dynamically stable character of Dirac MBenes. Electronic dispersions reveals that all Dirac MBenes exhibits finitely gapped Dirac cones at the fermi level, while FeB$_2$ MBene behaves as a zero-band-gap semimetal akin to graphene. Such gap in Dirac cones is desirable and crucial for optoelectronic applications. The interplay of out-of-plane $d_{xz}$ and $d_{yz}$ orbitals of metal atom and hybrids in-plane d$_{xy}$ and d$_{x^2-y^2}$ orbitals from metal atom with p orbitals from boron atoms can be attributed to the emergence of Dirac cones in MBenes. The calculations clearly reveal that the static dielectric constant and the energy gap within the Dirac cones are critical factors influencing the electron-hole screening effect, consequently effecting the exciton binding energy. Further, it has been demonstrated that the exciton binding energies are consistent with predictions made by the two-dimensional Mott-Wannier model, confirming the Mott-Wannier characteristics of excitons in AlB$_2$-type Dirac MBenes, with the exception of partial Frenkel character in FeB$_2$ MBene. Furthermore, it is demonstrated that Dirac MBenes exhibit a significant light absorption capacity in the near-infrared (NIR) and visible regions, with electron-hole interactions slightly modifying the optical spectral profile, making them promising for optoelectronic and photovoltaic applications. Subsequently, covariance analysis indicates that moderate energy gaps and high static dielectric constants are conducive to hosting Mott-Wannier excitons. Additionally, careful control of d-state valence electrons and hole doping can regulate the Mott-Wannier and Frenkel character of excitons in 2D Dirac materials. Thus, this comprehensive and systematic analysis of the electronic properties and optical-excitonic behavior of AlB$_2$-type Dirac MBenes, alongwith their correlations, enhances our understanding of this emerging family of two-dimensional materials.