Surface termination dependence of electronic and optical properties in Ti$_2$CO$_2$ MXene monolayers

Two-dimensional (2D) MXenes are a rapid growing family of 2D materials with rich physical and chemical properties where their surface termination plays an essential role. Among the various 2D MXenes, functionalization of the Ti$_{n}$C$_{n-1}$ phase with oxygen (O) atoms makes them attractive for optoelectronic applications due to their optical gap residing in the infrared or visible region. In this manuscript, we theoretically investigate the electronic and optical properties of four different O-atom-functionalized Ti$_{n}$C$_{n-1}$ MXene monolayers using state-of-the-art, first-principles techniques. In particular, we calculate the quasiparticle corrections on top of density functional theory (DFT) at the GW level and the exciton-dominated optical spectra by solving the Bethe-Salpeter equation (BSE) also at finite momentum. We find that all but one of the monolayer models are indirect band gap semiconductors where quasiparticle corrections are very important ($\sim 1$ eV). The optical spectra are instead dominated by direct and indirect excitons with large binding energies (between $0.5$ and $1$ eV). Most direct excitons lie above $1.5$ eV, while the indirect ones are below: therefore, we conclude that Ti$_{n}$C$_{n-1}$ should display strong absorption in the visible region, but phonon-assisted emission in the infrared. Our work thus reveals the potential usage of surface terminations to tune the optical and electronic properties of Ti$_{n}$C$_{n-1}$ MXene monolayers, while emphasizing the pivotal role of many-body effects beyond DFT to obtain accurate prediction for these systems.