Fig. 1. Crystal structure of monolayer TiO₂(a) top view; (b) side view; (c) K point path.

Fig. 2. Phonon spectrum of monolayer TiO₂.

Fig. 3. Molecular dynamics simulation of monolayer TiO₂.

Fig. 4. Polar coordinates for Young's modulus (left/blue line) and Poisson's ratio (right/red line) is the angle with respect to the a-direction.

Fig. 5. Energy band structure (left) and density of states (right) of (a) monolayer P-6M2 TiO₂, (b) monolayer rutile TiO₂, (c) monolayer anatase TiO₂.

Fig. 6. The differential charge density of monolayer TiO₂.

Fig. 7. (a) The relation between total energy and the applied strain along the a/b directions of monolayer TiO₂. The quadratic data fitting gives the in-plane stiffness of 2D structures. Black and red curves show the in-plane stiffness along the a and b directions of monolayer TiO₂. The shift of VBMs and CBMs for (b-c) monolayer TiO₂ with respect to the vacuum energy, as a function of the applied strain along either the a and b direction. The linear fit of the data yields the deformation potential constant.

Fig. 8. Band gap of monolayer TiO₂ under uniaxial/biaxial strain, calculated using the HSE06 functional.

Fig. 9. Schematic diagram of monolayer TiO₂ photocatalysis under uniaxial/biaxial strain.

Fig. 10. Optical properties: (a) virtual part of dielectric function; (b) absorption coefficient.

Table 2. Calculated effective mass , deformation potential constant , elastic modulus , and carrier mobility for monolayer TiO₂ along the a ( ) and b ( ) directions, where represents the position of the valence band top and the conduction band bottom.