Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron / Edition 1

by Shigeji Fujita, Kei Ito

Overview

The measurements of the Hall coefficient R and the Seebeck coefficient 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 coefficient R is negative H but the Seebeck coefficient 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 field (?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 field, 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 coefficient R H and positive Seebeck coefficient S.

Product Details

ISBN-13:	9781441925473
Publisher:	Springer New York
Publication date:	10/29/2010
Edition description:	Softcover reprint of hardcover 1st ed. 2007
Pages:	244
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

About the Author

Shigeji Fujita is Professor of Physics at State University of New York at Buffalo and has published 3 books with the Springer family since 1996. His areas of expertise include statistical physics, solid and liquid state physics, superconductivity and Quantum Hall Effect theory.

Kei Ito is also a Professor of Physics at the State University of New York at Buffalo, while on leave from the National Center for University Entrance Examinations in Tokyo, Japan.

Table 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.