The Structure and Properties of Matter

This book originally appeared in Japanese in 1973 in the Iwanami Series of Fundamental Physics supervised by Professor Hideki Yukawa and pub­ lished by Iwanami-Shoten. A revised second edition was published in 1978. The task we set ourselves was to grasp the properties of matter as a whole in a unified scheme and to present a general view of matter incor­ porating the results of modern physics. To achieve this goal we have tried to explore the laws which describe the structure of macroscopic matter, namely, to ask in what kinds of phy­ sical states matter can, in principle, exist and why. Thus, using the meth­ ods of statistical physics and quantum mechanics, we have tried to syste­ matically describe the properties of matter from a unified point of view. Of course, we do not believe that such a standpoint can give an exhaus­ tive description of condensed matter. One of the important viewpoints which obviously is omitted in such a unified approach is the historical one, which follows the development of physics in the course of time.

1. Atoms as Constituents of Matter.- 1.1 Introduction.- 1.2 Atomic Scale.- 1.3 One-Electron Atoms and the Hydrogen Atom.- 1.4 Central-Field Approximation.- 1.5 Shell Structure of Atoms and Periodicity of the Elements.- 1.6 Stationary States of Atoms I.- 1.7 Stationary States of Atoms II.- 2. System of Protons and Electrons.- 2.1 General Comments.- 2.2 Electronic State of a Hydrogen Molecule.- 2.3 Systems Made of Hydrogen Molecules.- 2.4 Metallic State at High Density.- 2.4.1 Electron-Electron Interaction.- 2.4.2 Interaction Between Protons and Electrons.- 2.4.3 Motion of Protons.- 2.5 Phase Diagram of the Proton-Electron System.- 3. Helium.- 3.1 Characteristics of Helium.- 3.2 Superfluidity.- 3.3 Phonons and Rotons.- 3.4 Liquid 3He; Fermi Liquid.- 3.4.1 Basic Ideas of the Fermi Liquid Theory.- 3.4.2 The Equilibrium Properties.- 4. Super fluid Helium 3.- 4.1 Basic Properties.- 4.1.1 Thermodynamic Properties.- 4.1.2 Transport Phenomena.- 4.1.3 Nuclear Magnetic Resonance (NMR) Experiments.- 4.2 Spin Triplet P-Wave Pairing.- 4.2.1 Cooper Pair.- 4.2.2 Generalization of the BCS Theory.- 4.2.3 Order Parameters of the Spin Triplet P-Wave Superfluid.- 4.2.4 ABM State and BW State.- 4.3 Physical Properties of ABM and BW States.- 4.3.1 Energy Gap.- 4.3.2 Normal (Super) Fluid Component ?n(?s).- 4.3.3 Susceptibility.- 4.4 Fermi Liquid Effects.- 4.5 Nuclear Spin Dynamics.- 4.5.1 Small Oscillations.- 4.5.2 Ringing.- 4.6 Texture and Superfluidity.- 5. Metals.- 5.1 Characteristics of Metals.- 5.2 Band Theory of Metals.- 5.3 Fermi Surface.- 5.4 Pseudopotential of Simple Metals.- 5.5 Structure of Simple Metals,.- 5.6 Transition Metals.- 5.7 Alloys.- 5.8 Superconductivity.- 6. Nonmetals.- 6.1 Molecular Crystals.- 6.2 Ionic Crystals.- 6.3 Covalent Crystal.- 6.4 Hydrogen-Bonded Crystals.- 6.5 Electron Theory of Nonmetals (Semiconductors).- 6.6 Semimetals.- 6.7 Properties of Matter Under High Pressure.- 7. Localized Electron Approximation.- 7.1 A Simple Model for Tetrahedrally Bonded Semiconductors.- 7.2 Bond Orbital Model (BOM).- 7.2.1 Effective Charge.- 7.2.2 Dielectric Constant.- 7.3 Cohesive Energy and Stability of Crystal Structures.- 7.4 Relationship Between the BOM and EPM.- 8. Magnetism.- 8.1 Magnetic Properties of Solids.- 8.2 Magnetic Properties of Simple Solids.- 8.3 Mechanism of Spin Polarization and the Electronic State in Solids.- 8.4 Configurations of Spin Polarization in Magnetic-Ordered States.- 8.4.1 Magnetic Anisotropy Energy and Crystal Fields.- 8.4.2 Magnetic Order in Insulators.- 8.4.3 Magnetic Order due to the Double Exchange Interaction.- 8.4.4 Magnetic Order in Metals.- 8.5 Collective Motion in Ordered States and Phase Transitions.- 8.6 Magnetic Properties of Dilute Alloys.- 8.7 Applications of Magnetic Measurements for Condensed Matter.- 9. Magnetic Properties of Dilute Alloys ― the Kondo Effect.- 9.1 Recent Investigations of the Kondo Effect.- 9.2 A Survey of Recent Experiments.- 9.3 Yosida-Yamada Theory.- 9.4 Renormalization Group Approach.- 10. Random Systems.- 10.1 Periodic and Aperiodic Systems.- 10.2 Point Defects.- 10.3 Line Imperfections and Dislocations.- 10.4 Cradle of Random Systems ― Melting of Crystals and Order-Disorder Phase Transition in Alloys.- 10.5 Noncrystalline Solids.- 10.6 Liquid Metals and Electronic and Vibrational States of Random Systems.- 11. Coherent Potential Approximation (CPA).- 11.1 Survey.- 11.2 A Few Examples of Experimental Results.- 11.2.1 Optical Absorption Spectra in Mixed Ionic Crystals.- 11.2.2 Photoemission of Transition Metal Alloys and Noble Metal Alloys.- 11.2.3 Magnetic Moments and Electron Specific Heat of Ferromagnetic Alloys.- 11.3 Computer Simulations and Exact Solutions.- 11.3.1 Results of Computer Experiments.- 11.3.2 Exact Results.- 11.4 Model Hamiltonian.- 11.5 One-Particle Green’s Function.- 11.6 Approximations before CPA.- 11.6.1 Rigid Band Model (the Lowest-Order Virtual Crystal Model).- 11.6.2 Virtual-Crystal Model.- 11.6.3 Dilute Limit.- 11.6.4 The Average t-Matrix Approximation (ATA).- 11.7 Derivation and the Characteristic Features of the CPA.- 11.7.1 Rigid Band Limit.- 11.7.2 Virtual-Crystal Limit.- 11.7.3 Dilute Limit.- 11.7.4 Split-Band Limit.- 11.8 Applications of the CPA.- 11.8.1 A One-Dimensional AB Alloy.- 11.8.2 Phonon Density of States of an Isotopically Disordered Model System.- 11.8.3 Density of States of a Three-Dimensional Alloy.- 11.8.4 Optical Absorption Spectra of Mixed Crystals.- 11.8.5 Density of States of Transition- and Noble-Metal Alloys.- 11.8.6 Ferromagnetic Alloys.- 11.9 Universality of the CPA.- 11.9.1 Cluster Effects (Multi-Site Approximations).- 11.9.2 Extension to Systems with Off-Diagonal Disorder.- 11.9.3 Extension to Systems with Both Diagonal and Off-Diagonal Disorder.- 11.9.4 Extension to Structurally Disordered Systems Composed of Single Species.- 11.9.5 Extension to the Multi-Band Hamiltonian.- 11.9.6 Extension of CPA to the Calculations of Other Physical Quantities.- References.