Odd-Frequency Superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ Measured by Kerr Rotation

We establish the existence of bulk odd-frequency superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and show that an intrinsic Kerr effect is direct evidence of this state. We use both general two- and three-orbital models, as well as a realistic tight-binding description of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ to demonstrate that odd-frequency pairing arises due to finite hybridization between different orbitals in the normal state, and is further enhanced by finite interorbital pairing.

Figure 1

Anomalous Green’s functions for ${\eta }_1=5$, ${\eta }_2={\eta }_3=2.5$, and ${\eta }_{23}=0.5$ with amplitudes (top) and complex phases (bottom), divided into (a) $F_{11}$ ($d_{xy}$), (b) $F_{22}$ ($d_{xz}$), (c) $F_{33}$ ($d_{yz}$), and interorbital (d) $F_{\mathrm{even}}$, and (e) $F_{\mathrm{odd}}$. The amplitude of $F_{\mathrm{odd}}$ is multiplied by 100.

Figure 2

Maximum amplitude of $F_{\mathrm{odd}}$ with changing order parameters ${\eta }_1$, ${\eta }_2$, and ${\eta }_{23}$. Nonchanging order parameters are fixed to ${\eta }_1=5$, ${\eta }_2={\eta }_3=2.5$, and ${\eta }_{23}=0.5$.

Figure 3

Anomalous Green’s function $F_{\mathrm{odd}}$ with amplitudes (top) and complex phases (bottom) for finite intraorbital pairing asymmetry using ${\eta }_2=2$ and ${\eta }_3=3$ with (a), (c) interorbital pairing ${\eta }_{23}=0.5$ and (b), (d) ${\eta }_{23}=0$. Also ${\eta }_1=5$.