Strain-enhanced superconductivity in RuO${}_2$ thin films: Joint experimental and theoretical studies

We investigate the superconducting properties of RuO${}_2$ films grown on TiO${}_2$ substrates by combining film fabrication and transport measurement with $\mathit{\text{ab}}\mathit{\text{initio}}$ calculation. Experimentally, we grow several RuO${}_2$ (110) thin films on TiO${}_2$ (110) substrates and observe superconductivity with critical temperature ($T_c$) of $\sim$2.0 K in 20-nm and 30-nm RuO${}_2$ (110) thin films. Theoretically, we study the superconductivity in both RuO${}_2$ (110) and RuO${}_2$ (100) epitaxial films within McMillan formalism of isotropic Migdal-Eliashberg theory. Among the salient results, the calculated phonon dispersion relations of all the considered RuO${}_2$ films show that the epitaxial films are dynamically stable. Importantly, our $\mathit{\text{ab}}\mathit{\text{initio}}$ calculations reveal that independent of the film orientation, the [001] compressive strain ${\epsilon }_{[001]}$ pushes the flat Ru $d_{z^2}$-dominant bands towards the Fermi level ($E_F$), 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 RuO${}_2$ films. Remarkably, the amount of the phonon softening and the enhanced $T_c$ increase almost linearly with the increasing ${\epsilon }_{[001]}$. The calculated $T_c$ for the films with thickness of $\ge$ 20 nm agree well with the experimental $T_c$. These findings demonstrate that among other things, lattice mismatch strain provides an effective route for tuning phonon-mediated superconductivity in RuO${}_2$ and other thin films.