Mechanism of plain s-wave superconductivity in heavy fermion compounds near magnetic criticality: Impact of vertex corrections for gap equation

We study the orbital-fluctuation-mediated pairing mechanism in heavy fermion systems, motivated by the recent experimental repots of emerging the plane s-wave state without sign-reversal in CeCu2Si2. For this purpose,
we study the recently developed improved gap equation on the basis of the multiorbital periodic Anderson model in the presence of strong spin-orbit interaction (SOI). We take account of the vertex correction for the bare Coulomb interaction (U-VC), which represents the higher-order many-body-effects beyond the Migdal-Eliashberg approximation [1]. We find that the plain s-wave state is realized against the strong Coulomb interaction since the orbital-fluctuation-mediated attractive interaction, driven by the VCs and the e-ph interactions, is strongly enhanced by the U-VC. Near the magnetic criticality, the U-VC becomes significant due to the Aslamazov-Larkin process, which is analogous to the Kugel-Khomskii orbital-spin coupling term in the strong-coupling model. We conclude that the plain s-wave state is realized in multiorbital heavy-fermion systems since the strong SOI magnifies the U-VC in 4f electron systems. [1] R.tazai, Y. Yamakawa, and H. Kontani, J. Phys, Soc. Jpn. 86, 073703 (2017).