We investigate the superconducting properties of ${\mathrm{RuO}}_2$ films grown on ${\mathrm{TiO}}_2$ substrates by combining film fabrication and transport measurement with $\mathrm{ab\; initio}$ calculation. Experimentally, we grow several ${\mathrm{RuO}}_2$ (110) thin films on ${\mathrm{TiO}}_2$ (110) substrates and observe superconductivity with critical temperature ($T_c$) of ∼2.0 K in 20-nm and 30-nm ${\mathrm{RuO}}_2$ (110) thin films. Theoretically, we study the superconductivity in both ${\mathrm{RuO}}_2$ (110) and ${\mathrm{RuO}}_2$ (100) epitaxial films within McMillan formalism of isotropic Migdal-Eliashberg theory, using the normal state properties from $\mathrm{ab\; initio}$ calculations. The crystal structures of the films are obtained with the out-of-plane lattice constant and atomic positions determined by ab initio calculations while the in-plane lattice constants held fixed to the experimental values. Among the salient results, the calculated phonon dispersion relations of all the considered ${\mathrm{RuO}}_2$ films have no imaginary frequencies, i.e., the epitaxial films are dynamically stable. Importantly, our ab initio calculations reveal that, independent of the film orientation, the [001] compressive strain ${\epsilon }_{\left[001\right]}$ pushes the flat Ru $d_{z^2}$-dominant bands towards the Fermi level $\left(E_F\right)$ and significantly soften the out-of-plane acoustic phonon mode near the R point in the Brillouin zone, which substantially enhances the electron-phonon coupling (EPC) strength $\lambda$ and hence the calculated $T_c$ in the ${\mathrm{RuO}}_2$ films. Remarkably, the amount of the phonon softening and the enhanced $T_c$ increase almost linearly with the increasing ${\epsilon }_{\left[001\right]}$. The calculated $T_c$ for the films with thickness $t\ge 20\mathrm{nm}$ agree well with the experimental $T_c$. For example, the theoretical $T_c$ of 2.8 K for 20-nm ${\mathrm{RuO}}_2$ (110) film and 0.8 K for 28-nm ${\mathrm{RuO}}_2$ (100) film are close to the experimental $T_c$ of 2.0 K and 1.0 K, respectively. These findings demonstrate that, among other things, lattice mismatch strain provides an effective route for tuning phonon-mediated superconductivity in ${\mathrm{RuO}}_2$ and other thin films.

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• Phonons
• Superconductivity
• Transition temperature
• Electrical transport techniques
• First-principles calculations
• X-ray diffraction