Abstract
In this chapter, we study a microscopic origin of fully gapped s-wave superconductivity (SC) in multipole heavy fermion system CeCu\(_2\)Si\(_2\). First, we show that various magnetic (\(=\) odd-rank) multipole fluctuations develop simultaneously near the anti-ferromagnetic phase (AFM). It originates from the cooperation between strong spin-orbit coupling and on-site Coulomb repulsion. Then, the enhanced magnetic fluctuations give violation of Migdal-Eliashberg approximation. In particular, higher order many body effects, called vertex corrections (VC), become important. We find that VC for bare Coulomb repulsion enhance attractive pairing interaction. As a result, s-wave superconducting gap without any sign reversal appears near the AFM phase. Furthermore, the s-wave state is stabilized in the presence of moderate phonon-induced electric fluctuations. The present study will be helpful to understand the recent experimental discovery on CeCu\(_2\)Si\(_2\).
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