Development of a two-particle self-consistent method for multi-orbital systems and its application to unconventional superconductors

We extend the two-particle self-consistent method proposed by Vilk and Tremblay [1] to multi-orbital systems. Starting with the sum rules for the spin and charge susceptibilities, we derive self-consistent equations to determine the renormalized effective interactions. We apply this method to LaFeAsO. In the former, we study the two-orbital model for the La$_{2-x}$(Sr/Ba)$_x$CuO$_4$ system. FLEX underestimated the pairing instability for it.[2] We show that, in our TPSC, the inter-orbital scattering enhances the d-wave instability. In the latter, we investigate a five-orbital d-model for LaFeAsO. This model has been extensively studied by RPA [3]. There, it has been shown that strong spin fluctuation mediates the s$_{+-}$ superconductivity. On the other hand, it has been pointed out that vertex corrections can enhance orbital fluctuations, which mediate s$_{++}$ superconductivity [4]. Finally, we show that orbital fluctuations can be enhanced in TPSC, while the dominant pairing symmetry is still s$_{+-}$ superconductivity when the system resides.\\[4pt] [1] Y.M. Vilk, A.-M.S. Tremblay, J. Phys. I France 7, 13091368.\\[0pt] [2] H. Sakakibara, et al, Phys. Rev. Lett. 105, 057003.\\[0pt] [3] K. Kuroki, et al, Phys. Rev. Lett. 101, 087004.\\[0pt] [4] H. Kontani and S. Onari, Phys. Rev. Lett. 104, 157001.