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 \textit{ab 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 \textit{ab initio} calculations reveal that independent of the film orientation, the [001] compressive strain $ε_{[001]}$ 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 $λ$ 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 $ε_{[001]}$. The calculated $T_c$ for the films with thickness of $\geq$ 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.