Fully gapped s-wave superconductivity enhanced by magnetic criticality in heavy fermion system

In heavy fermion systems, higher-rank multipole operators are active thanks to the strong spin-orbit interaction (SOI), and the role of diverse multipole fluctuations on the pairing mechanism attracts a lot of attention. Here, we study a mechanism of superconductivity in heavy fermion systems, by focusing on the impact of vertex corrections (VCs) for the pairing interaction going beyond the Migdal approximation. In heavy fermion systems, strong interference between multipole fluctuations cause significant VCs, that represent many-body effects beyond mean-field-type approximations. Especially, the coupling constants between electrons and charged-bosons, including the electron-phonon coupling constant, are strongly magnified by the VCs. For this reason, moderate even-rank (=electric) multipole fluctuations give large attractive interaction, and therefore s-wave superconductivity can emerge in heavy-fermion systems. In particular, phonon-mediated superconductivity is expected to be realized near the magnetic criticality, thanks to the VCs due to magnetic multipole fluctuations. The present mechanism may be responsible for the fully gapped s-wave superconducting state realized in CeCu2Si2.