Thickness-dependent superconductivity and quantum spin Hall effects in ${\mathrm{Ti}}_{n+1}{O}_n$ ($n$ = 2, 3) MOenes

MXene-like MOenes have shown intriguing properties, such as superconductivity in ${\mathrm{Ti}}_{2}O$ monolayers, direct band gaps, exotic quantum phase transitions, and strong light harvesting in ${\mathrm{Ti}}_{2}O{X}_2$ ($X$ = F, Cl) monolayers. However, stoichiometry engineering as a commonly tunable factor should be extended to study the thickness-dependent properties of MOenes. In this study, ${\mathrm{Ti}}_{n+1}{O}_n$ ($n$ = 2, 3) MOenes and their functionalized counterparts are systematically investigated using ab initio calculations. Similar to the $2H\text{−}{\mathrm{Ti}}_{2}O$ monolayer with a superconducting transition temperature $T_c$ of 4.7 K, $2H\text{−}{\mathrm{Ti}}_3{O}_2$ and ${\mathrm{Ti}}_4{O}_3$ monolayers are superconductors with a $T_c$ of 4.4 and 3.7 K, respectively. More interestingly, $2H\text{−}{\mathrm{Ti}}_3{O}_2{F}_2$ and ${\mathrm{Ti}}_4{O}_3{F}_2$ monolayers exhibit quantum spin Hall effects at room temperature with nontrivial gaps of 0.22 and 0.20 eV, respectively. The $d\text{−}d$ band inversion mechanism is crucial for their topological nature. Therefore, the thickness-dependent features in ${\mathrm{Ti}}_{n+1}{O}_n$ MOenes will draw more attention to this emerging family of MOenes.