Excitons, optical spectra, and electronic properties of semiconducting Hf-based MXenes

Semiconducting MXenes are an intriguing two-dimensional (2D) material class with promising electronic and optoelectronic properties. Here, we focused on recently prepared Hf-based MXenes, namely Hf$_3$C$_2$O$_2$ and Hf$_2$CO$_2$. Using the first-principles calculation and excited state corrections, we proved its dynamical stability, reconciled its semiconducting behavior, and obtained fundamental gaps by the many-body GW method (indirect 1.1 eV and 2.2 eV, respectively, direct 1.4 eV and 3.5 eV, respectively). Using the Bethe-Salpeter equation (BSE) we subsequently provided optical gaps (0.9 eV and 2.7eV, respectively), exciton binding energies, absorption spectra, and other properties of excitons in both Hf-based MXenes. The indirect character of both 2D materials further allowed a significant decrease of excitation energies by considering indirect excitons with exciton momentum along the $\Gamma$-M path in the Brillouin zone. The first bright excitons are strongly delocalized in real space while contributed by only a limited number of electron-hole pairs around the M point in the k-space from the valence and conduction band. A diverse range of excitonic states in Hf$_3$C$_2$O$_2$ MXene lead to a 4\% and 13\% absorptance for the first and second peaks in the infrared region of absorption spectra, respectively. In contrast, a prominent 28\% absorptance peak in the visible region appears in Hf$_2$CO$_2$ MXene. Results from radiative lifetime calculations indicate the promising potential of these materials in optoelectric devices requiring sustained and efficient exciton behavior.