Theory of multipolar order and unconventional superconductivity in heavy fermion systems; importance of nonlocal vertex corrections

In heavy-fermion systems, higher-rank multipole operators are active thanks to the strong spin-orbit interaction (SOI). Therefore, multipole fluctuations cause rich quantum critical phenomena, such as unconventional superconductivity and hidden-order phase. However, the microscopic pictures of these phenomena have not been fully understood. To solve these issues, we study higher-rank multipole fluctuations by considering the vertex corrections (VCs), which represent higher-order many body effects, on the basis of multi-orbital Periodic Anderson Model [1]. We find that the significant effects are given by Aslamazov-Larkin process, which originate from strong interference between multipole fluctuations. Due to the AL-VC, various types of multipole fluctuations develop simultaneously near the magnetic QCP. Especially, some electric multipole (quadrupole or hexadecapole) fluctuations are drastically enlarged, which remain small in mean field theories. Thus, various interesting phase due to the electric multipole fluctuations are expected to be realized in heavy fermion systems. In this talk, we discuss both the s-wave superconductivity in CeCu₂Si₂ [1] and the hidden-order phase in CeB₆, which are reported by recent improved experiments. [1] R. tazai and H. kontani, arXiv:1807.11427.