Spin-Triplet Superconductivity in Sr$_2$RuO$_4$ due to Orbital and Spin Fluctuations: 2D fRG Analysis

We study the mechanism of the triplet superconductivity in Sr$_2$RuO$_4$, by applying the functional renormalization group (fRG) method to the multi-orbital Hubbard model [1]. Thanks to the vertex correction, we observe the strong spin and orbital fluctuations at $Q \approx (2\pi/3, 2\pi/3)$ in the quasi-one-dimensional Fermi surfaces (which are composed of $d_{xz}$ and $d_{yz}$ orbitals). Moreover, due to the cooperation of spin and orbital fluctuations, the triplet superconductivity emerges where the superconducting gap is given by the linear combination of $(\Delta_x (k), \Delta_y (k)) \approx (\sin 3k_x, \sin 3k_y)$ [2]. These results can also be confirmed by a diagrammatic calculation of the vertex correction. \\ \noindent [1] M. Tsuchiizu, Y. Ohno, S. Onari, and H. Kontani, PRL \textbf{111}, 057003 (2013). \\ \noindent [2] M. Tsuchiizu, Y. Yamakawa, Y. Ohno, S. Onari, and H. Kontani, arXiv:1405.2028.