Theory of Multipole Fluctuation Mediated Superconductivity and Multipole Phase: Important Roles of Many Body Effects and Strong Spin-Orbit Coupling (Springer Theses)

A strong spin-orbit interaction and Coulomb repulsion featuring strongly correlated d - and f -electron systems lead to various exotic phase transition including unconventional superconductivity and magnetic multipole order. However, their microscopic origins are long standing problem since they could not be explained based on conventional Migdal-Eliashberg theorem. The book focuses on many-body correlation effects beyond conventional theory for the d - and f -electron systems, and theoretically demonstrates the correlations to play significant roles in “mode-coupling” among multiple quantum fluctuations, which is called U - VC here. The following key findings are described in-depth: (i) spin triplet superconductivity caused by U - VC , (ii) being more important U - VC in f -electron systems due to magnetic multipole degrees of freedom induced by a spin-orbit interaction, and (iii) s -wave superconductivity stabilized cooperatively by antiferromagnetic fluctuations and electron-phonon interaction contrary to conventional understanding. The book provides meaningful step for revealing essential roles of many-body effects behind long standing problems in strongly correlated materials. Supervisor’s Foreword Preface Parts of this thesis have been published in the following journal articles: Acknowledgements Contents Acronyms 1 Common Introduction 1.1 Superconductivity in SCES 1.2 Multipole Degrees of Freedom References Part I d-electron Systems 2 Functional Renormalization Group (fRG) Study 2.1 Background 2.2 Formalism 2.2.1 Multi-Orbital Hubbard Model 2.2.2 Four-Point Vertex Function 2.2.3 Three-Point Vertex Function 2.3 Results 2.3.1 Emergence of Triplet Superconductivity 2.3.2 SC Pairing Interaction 2.3.3 Significant Roles of U-VC 2.3.4 Perturbation Theory 2.4 Summary References 3 Cooperation of el-ph and AFM Fluctuations 3.1 Background 3.1.1 el-ph Versus AFM Fluctuation 3.2 Formalism 3.2.1 Hubbard-Holstein Model (B1g Phonon) 3.2.2 Phonon-Mediated Electric Interaction 3.2.3 Susceptibility with Self-Consistent Vertex Correction 3.3 Results 3.3.1 B1g-Orbital Fluctuations 3.3.2 Superconductivity 3.3.3 Momentum Dependence of U-VC 3.3.4 Filling Dependence 3.3.5 Retardation and Impurity Effects 3.4 Summary References Part II f-electron Systems 4 Fully Gapped Superconductivity in CeCu2Si2 4.1 Background 4.2 Formalism 4.2.1 Multi-Orbital Periodic Anderson Model 4.2.2 Multipole Symmetry 4.2.3 Multipole Susceptibility 4.2.4 Phonon-Mediated Interaction 4.3 Results 4.3.1 SC Phase Diagram 4.3.2 U-VC 4.3.3 CEF Splitting and f-f Hopping 4.3.4 Microscopic Origin of s-wave SC 4.3.5 Retardation Effect 4.4 Summary References 5 Multipole Phase 5.1 Background 5.2 Formalism 5.3 Results 5.3.1 Magnetic Multipole Susceptibility 5.3.2 Electric Multipole Susceptibility 5.4 Discussion 5.4.1 Microscopic Origin of Quadrupole Phase 5.4.2 Magnetic Field References 6 Summary of This Book Appendix Curriculum Vitae