Quantum Theory of Conducting Matter : Newtonian Equations of Motion for a Bloch Electron

The measurements of the Hall coe?cient R and the Seebeck coe?cient H (thermopower) S are known to give the sign of the carrier charge q. Sodium (Na) forms a body-centered cubic (BCC) lattice, where both R and S are H negative, indicating that the carrier is the “electron. ” Silver (Ag) forms a face-centered cubic (FCC) lattice, where the Hall coe?cient R is negative H but the Seebeck coe?cient S is positive. This complication arises from the Fermi surface of the metal. The “electrons” and the “holes” play important roles in conducting matter physics. The “electron” (“hole”), which by de?- tion circulates counterclockwise (clockwise) around the magnetic ?eld (?ux) vector B cannot be discussed based on the prevailing equation of motion in the electron dynamics: dk/dt = q(E +v×B), where k = k-vector, E = electric ?eld, and v = velocity. The energy-momentum relation is not incorporated in this equation. In this book we shall derive Newtonian equations of motion with a s- metric mass tensor. We diagonalize this tensor by introducing the principal masses and the principal axes of the inverse-mass tensor associated with the Fermi surface. Using these equations, we demonstrate that the “electrons” (“holes”) are generated, depending on the curvature sign of the Fermi s- face. The complicated Fermi surface of Ag can generate “electrons” and “holes,” and it is responsible for the observed negative Hall coe?cient R H and positive Seebeck coe?cient S. Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron targets scientists, researchers and graduate-level students focused on experimentation in the fields of physics, chemistry, electrical engineering, and material sciences. It is important that the reader have an understanding of dynamics, quantum mechanics, thermodynamics, statistical mechanics, electromagnetism and solid-state physics. Many worked-out problems are included in the book to aid the reader's comprehension of the subject. The Bloch electron (wave packet) moves by following the Newtonian equation of motion. Under an applied magnetic field B the electron circulates around the field B counterclockwise or clockwise depending on the curvature of the Fermi surface. The signs of the Hall coefficient and the Seebeck coefficient are known to give the sign of the major carrier charge. For alkali metals, both are negative, indicating that the carriers are "electrons." These features arise from the Fermi surface difference. The authors show an important connection between the conduction electrons and the Fermi surface in an elementary manner in the text. No currently available text explains this connection. The authors do this by deriving Newtonian equations of motion for the Bloch electron and diagonalizing the inverse mass (symmetric) tensor. The currently active areas of research, high-temperature superconductivity and Quantum Hall Effect, are important subjects in the conducting matter physics, and the authors plan to follow up this book with a second, more advanced book on superconductivity and the Quantum Hall Effect. Introduction -- Lattice Vibrations And Heat Capacity -- Free Electrons And Heat Capacity -- Electric Conduction And The Hall Effect -- Magnetic Susceptibility -- Boltzmann Equation Method -- Bloch Theorem -- The Fermi Liquid Model -- The Fermi Surface -- Bloch Electron Dynamics -- De Haas-van Alphen Oscillations -- Magnetoresistance -- Cyclotron Resonance -- Seebeck Coefficient (thermopower) -- Infrared Hall Effect. Shigeji Fujita And Kei Ito. Includes Bibliographical References (p. 227-235) And Index. Quantum Theory of Conducting Matter 2 Preface 6 Contents 10 Constants, Signs, Symbols, andGeneral Remarks 14 Part I Preliminaries 21 Part II Bloch Electron Dynamics 99 Part III ApplicationsFermionic Systems (Electrons) 144 Appendix A Electromagnetic Potentials 226 Appendix B Statistical Weight for theLandau States 230 Appendix C Derivation of Equation (11.19) 233 References 234 Bibliography 239 Index 242 Shows an important connection between the conduction electrons and the Fermi surface in an elementary manner. This title is intended for scientists, researchers and graduate-level students focused on experimentation in the fields of physics, chemistry, electrical engineering, and materials science