Thickness-dependent superconductivity and quantum spin Hall effects in Ti n + 1 O n ( n = 2, 3) MOenes

MXene-like MOenes have shown intriguing properties, such as superconductivity in ${\mathrm{Ti}}_{2}\mathrm{O}$ monolayers, direct band gaps, exotic quantum phase transitions, and strong light harvesting in ${\mathrm{Ti}}_{2}\mathrm{O}{X}_{2}$ ($X$ = 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, ${\mathrm{Ti}}_{n+1}{\mathrm{O}}_{n}$ ($n$ = 2, 3) MOenes and their functionalized counterparts are systematically investigated using ab initio calculations. Similar to the $2H\text{\ensuremath{-}}{\mathrm{Ti}}_{2}\mathrm{O}$ monolayer with a superconducting transition temperature ${T}_{c}$ of 4.7 K, $2H\text{\ensuremath{-}}{\mathrm{Ti}}_{3}{\mathrm{O}}_{2}$ and ${\mathrm{Ti}}_{4}{\mathrm{O}}_{3}$ monolayers are superconductors with a ${T}_{c}$ of 4.4 and 3.7 K, respectively. More interestingly, $2H\text{\ensuremath{-}}{\mathrm{Ti}}_{3}{\mathrm{O}}_{2}{\mathrm{F}}_{2}$ and ${\mathrm{Ti}}_{4}{\mathrm{O}}_{3}{\mathrm{F}}_{2}$ monolayers exhibit quantum spin Hall effects at room temperature with nontrivial gaps of 0.22 and 0.20 eV, respectively. The $d\text{\ensuremath{-}}d$ band inversion mechanism is crucial for their topological nature. Therefore, the thickness-dependent features in ${\mathrm{Ti}}_{n+1}{\mathrm{O}}_{n}$ MOenes will draw more attention to this emerging family of MOenes.