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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.
List of contents
Preliminaries.- Lattice Vibrations and Heat Capacity.- Free Electrons and Heat Capacity.- Electric Conduction and the Hall Effect.- Magnetic Susceptibility.- Boltzmann Equation Method.- Bloch Electron Dynamics.- Bloch Theorem.- The Fermi Liquid Model.- The Fermi Surface.- Bloch Electron Dynamics.- Applications Fermionic Systems (Electrons).- De Haas-Van Alphen Oscillations.- Magnetoresistance.- Cyclotron Resonance.- Seebeck Coefficient (Thermopower).- Infrared Hall Effect.
About the author
Shigeji Fujita was awarded his Ph.D. degree in physics from the University of Maryland at College Park in 1960. He subsequently worked as a research assistant and assistant professor at various Japanese and American universities and held visiting appointments at universities around the world. In 1968, he was appointed to a professorship at the Department of Physics of the State University of New York at Buffalo, which is where he still teaches. Professor Fujita conducts research in several areas, among others in equilibrium and non-equilibrium statistical mechanics, the Kinetic Theory of plasmas, gases, liquids and solids, and the Quantum Hall Effect. He has published over 200 articles and eleven books.
Summary
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.
