Effects of strain in multiorbital superconductors: The case of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

Uniaxial-strain experiments have become a powerful tool to unveil the character of unconventional phases of electronic matter. Here, we propose a combination of the superconducting fitness analysis and density functional theory calculations to dissect the effects of strain in complex multiorbital quantum materials from a microscopic perspective. We apply this framework to the superconducting state of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and argue that the recently proposed orbitally antisymmetric spin triplet order parameter candidate has unique signatures under strain which are in agreement with recent observations. In particular, we can account for the asymmetric splitting of the critical temperatures for compressive strain along the $\langle 100\rangle$ direction and the reduction of the critical temperature for compressive strain along the $\langle 001\rangle$ and $\langle 110\rangle$ directions with a single free parameter.

Figure 1

Fermi surfaces indicating the orbital distribution for unstrained ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ in the $k_z=0$ plane. The color red (blue, green) encodes the orbital $d_{xy}$ ($d_{yz}$, $d_{xz}$) content as low (bright) or high (dark) color in each Fermi surface sheet. The data are obtained by combining the ab initio-derived tight-binding Hamiltonian with a local correlation-enhanced effective spin-orbit coupling term ($\lambda =0.2$ eV) [51].

Figure 2

Evolution of $T_c$ and $T_{\text{TRSB}}$ under compressive uniaxial strain along the $\langle 100\rangle$, $\langle 001\rangle$, and $\langle 110\rangle$ directions for the order parameter $\left\{\right[5,3],[6,3\left]\right\}$, (a) with $g=5.8$ and (b) setting $F_1=F_2=0$ for $g=5$. The horizontal dotted line is a guide to the eye corresponding to the unstrained critical temperature. The black and red (blue) circles at $s=-0.5\%$ ($s=-0.2\%$) correspond to the experimental value for strain along the $\langle 100\rangle$ and $\langle 001\rangle$ ($\langle 110\rangle$) directions obtained from Refs. [12, 27] ([28]), respectively. We took the Young's modulus along the $\langle 001\rangle$ direction to be approximately $200\mathrm{GPa}$. For both plots we set the representative $k_F=2.67$ to be between the $\beta$ and $\gamma$ Fermi surfaces.