Quantum Critical Phenomena of Valence Transition: Heavy Fermion Metals and Related Systems (Springer Tracts in Modern Physics, 289)

This book comprehensively presents an unconventional quantum criticality caused by valence fluctuations, which offers theoretical understanding of unconventional Fermi-liquid properties in cerium- and ytterbium-based heavy fermion metals including CeCu 2 (Si,Ge) 2 and CeRhIn 5 under pressure, and quasicrystal β-YbAlB 4 and Yb 15 Al 34 Au 51 . The book begins with an introduction to fundamental concepts for heavy fermion systems, valence fluctuation, and quantum phase transition, including self-consistent renormalization group theory. A subsequent chapter is devoted to a comprehensive description of the theory of the unconventional quantum criticality based on a valence transition, featuring explicit temperature dependence of various physical quantities, which allows for comparisons to relevant experiments. Lastly, it discusses how ubiquitous the valence fluctuation is, presenting candidate materials not only in heavy fermions, but also in strongly correlated electrons represented by high- T c superconductor cuprates. Introductory chapters provide useful materials for learning fundamentals of heavy fermion systems and their theory. Further, experimental topics relevant to valence fluctuations are valuable resources for those who are new to the field to easily catch up with experimental background and facts. Preface Acknowledgements Contents 1 Prologue 1.1 Conventional Valence Transition 1.1.1 Ce Metal 1.1.2 YbInCuSubscript 44 1.2 Quantum Critical Valence Fluctuations 1.3 Brief Summary of Chapters Discussed in This Monograph References 2 Early History of Critical Valence Fluctuations 2.1 Anomalous Response of Physical Quantities Under Pressure 2.1.1 Drastic Decrement of upper AA-Coefficient in Resistivity 2.1.2 Sharp Crossover of Kadowaki-Woods Ratio upper A divided by gamma squaredA/γ2 2.1.3 Huge Enhancement of Residual Resistivity 2.1.4 Direct Experimental Evidence of Sharp Valence Transition 2.1.5 Birds Eye View of Early History References 3 Fundamentals of Heavy Fermion State 3.1 Heavy Fermion Systems 3.1.1 Fermi Gas and Fermi Liquid 3.1.2 Behaviors of Heavy Fermions at Low Temperatures 3.2 Origin of Heavy Electron State: Intuitive Understanding 3.3 Representation of Quasiparticles by Green Function 3.4 Heavy Fermion System as Fermi Liquid 3.4.1 Periodic Anderson Model 3.4.2 Heavy Electrons as Quasiparticles 3.4.3 One-Particle Spectral Weight of 4f Electron 3.5 Kadowaki-Woods Relation References 4 Anomalous Phenomena Due to Critical Valence Transition 4.1 Extended Anderson Lattice Model for Valence Transition 4.2 Anomalies in Resistivity and Specific Heat 4.2.1 upper TT-linear Resistivity and Enhanced Sommerfeld Coefficient at upper P equals upper P Subscript normal vP=Pv 4.3 Trends of Unconventional Superconductivity 4.4 Results on Microscopic Treatments of Extended PAM 4.4.1 Superconductivity Induced by Critical Valence Fluctuations 4.4.2 Mean-Field Solution for Valence Change 4.5 DMRG Calculation 4.6 Effect of Magnetic Field on Valence Transition and Valence Crossover 4.6.1 Magnetic Field Dependence of First-Order Valence Transition 4.6.2 Field Induced Quantum Critical Point of the Valence Transition 4.6.3 Comparison with Experiments 4.6.4 Consequence of Field Induced Valence QCP References 5 Self-consistent Renormalization Theory 5.1 Magnetism in Itinerant Electron Systems with Electron Correlations 5.2 Perturbation Renormalization Group Approach 5.3 Mode-Coupling Theory for Magnetic Fluctuations 5.3.1 SCR Theory in Path-Integral Formalism 5.3.2 Effect of Mode-Mode Coupling of Spin Fluctuations 5.3.3 Solution of the SCR Equation and Criticality 5.3.4 Entropy and Specific Heat 5.3.5 Thermal-Expansion Coefficient 5.3.6 Grüneisen Parameter 5.3.7 Comparison with Experiments References 6 Quantum Criticality of Valence Transition—Experiments and Theory 6.1 Systematic Anomalies Associated with Critical Valence Transition 6.2 The Action Derived from the Extended Anderson Lattice Model 6.3 Perturbation Renormalization Group Approach 6.4 Mode-Coupling Theory for Critical Valence Fluctuations 6.4.1 NMR Relaxation Rate 6.4.2 Resistivity 6.4.3 Specific Heat 6.4.4 Thermal Expansion Coefficient 6.4.5 Grüneisen Parameter 6.5 upper T divided by upper BT/B Scaling in Temperature and Magnetic Field of Magnetization 6.5.1 Mode Coupling Theory of Valence Fluctuations Under Magnetic Field for betaβ-YbAlBSubscript 44 6.5.2 Direct Observation of Quantum Valence Criticality in alphaα-YbAlSubscript 1 minus x1-xFeSubscript xxBSubscript 44 left parenthesis x equals 0.014 right parenthesis(x=0.014) 6.5.3 On the Yb Valence in Yb(RhSubscript 1 minus x1-xCoSubscript xx)Subscript 22SiSubscript 22 6.6 Case Study of Critical Valence Transition: Quasicrystal Heavy Fermion ... 6.6.1 Robust Quantum Criticality Under Pressure 6.6.2 Origin of Quantum Criticality and upper T divided by upper BT/B Scaling 6.6.3 Non-divergent Grüneisen Parameter in Quantum Critical Quasicrystal 6.6.4 Elastic Softening in Quantum Critical Yb-Al-Au Approximant Crystal and Quasicrystal 6.6.5 Lattice Constant Dependence of Yb Valence 6.6.6 Direct Observation of Quantum Valence Criticality in Quasicrystal and Pressurized Approximant References 7 Interplay Between Magnetic QCP and Valence QCP 7.1 Drastic Change of Fermi Surface in CeRhInSubscript 55 Under Pressure 7.1.1 Experiments in CeRhInSubscript 55 7.1.2 Theory Treating Equal Footing of Magnetic and Valence Transitions 7.2 Comprehensive Understanding of the Phase Diagram of the Heavy ... References 8 Instead of Epilogue—Ubiquity of Critical Valence Fluctuations 8.1 Candidate Materials in Which Critical Valence Transition ... 8.1.1 YbCuSubscript 5 minus x5-xAlSubscript xx 8.1.2 Direct Observation of 4f-5d Coulomb Repulsion in Rare-Earth Atom 8.1.3 CeCuSubscript 66 8.1.4 Ce(Ir,Rh)SiSubscript 33 8.1.5 Ce(Co,Rh,Ir)InSubscript 55 8.1.6 Compounds with Sharp Enhancement of Residual Resistivity rho 0ρ0 References Appendix A Distribution Function of Fermions Appendix B Coefficient of the Gaussian Term—Derivation of upper C Subscript qCq in Eq. (5.17摥映數爠eflinkeq:kaispsqspsw5.175) in Chap.5 Appendix C Quantum Criticality in the SCR Theory C.1 Quantum Criticality in d equals 3d=3 C.2 Solution of SCR Equation for z equals 3z=3 in d equals 2d=2 C.3 Equivalence of SCR Solution and Renormalization Group for z equals 2z=2 in d equals 2d=2 Appendix D Thermal-Expansion Coefficient and Grüneisen Parameter D.1 Thermal-Expansion Coefficient D.2 Grüneisen Parameter Appendix E Electric Quadrupole Susceptibility Near the Valence QCP References Index