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In heavy fermion systems, higher-rank multipole operators are active thanksto the strong spin-orbit interaction (SOI), and the role of diverse multipolefluctuations on the pairing mechanism attracts a lot of attention. Here, westudy a mechanism of superconductivity in heavy fermion systems, by focusing onthe impact of vertex corrections (VCs) for the pairing interaction going beyondthe Migdal approximation. In heavy fermion systems, strong interference betweenmultipole fluctuations cause significant VCs, that represent many-body effectsbeyond mean-field-type approximations. Especially, the coupling constantsbetween electrons and charged-bosons, including the electron-phonon couplingconstant, are strongly magnified by the VCs. For this reason, moderateeven-rank (=electric) multipole fluctuations give large attractive interaction,and therefore s-wave superconductivity can emerge in heavy-fermion systems. Inparticular, phonon-mediated superconductivity is expected to be realized nearthe magnetic criticality, thanks to the VCs due to magnetic multipolefluctuations. The present mechanism may be responsible for the fully gappeds-wave superconducting state realized in CeCu2Si2.

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