Theory of superconductivity and anomalous Hall effect in Multi-pole system CeCu₂Si₂

In heavy fermion system, multipole degree of freedom induce interesting phenomena, such as unconventional superconductivity (SC) and Anomalous Hall Effect (AHE). Recent experiments have revealed that unconventional s-wave SC state without any sigh-reversal emerges near the AFM phase in heavy fermion compound CeCu₂Si₂. However, this fact cannot be explained by conventional Migdal-Eliashberg (ME) theory. To overcome this difficulty, we study the microscopic SC paring mechanism in the presence of strong spin-orbit interaction (SOI) and higher-order many body effects ignored in ME theory. As a result, we find that unconventional s-wave state is realized near the AFM phase against the strong magnetic fluctuations. Moreover, obtained s-wave SC originates from interference between electric and magnetic multipole fluctuations due to the mode coupling effects given by many body effects. In addition, we propose large AHE will be induced due to the multi-orbital nature and strong SOI in the present system. [1] R. Tazai and H. kontani, J. Phys, Soc. Jpn. 88, 063701 (2019).