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Quantum Theory of Conducting Matter

Newtonian Equations of Motion for a Bloch Electron

  • Book
  • © 2007

Overview

Authors:
  1. Shigeji Fujita

    1. Department of Physics, University at Buffalo, The State University of New York, Buffalo, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Kei Ito

    1. Research Division, The National Center for University Entrance Examinations, Tokyo, Japan

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    You can also search for this author in PubMed   Google Scholar

  • Current solid-state physics books say very little about the dynamics of Bloch electrons, and this book will help users to learn and master the issue
  • The book brings together various modern concepts at the forefront of condensed matter physics including the connection between conduction electrons and the Fermi surface
  • The book will be followed up by a more advanced book on superconductivity and the Quantum Hall Effect
  • Includes supplementary material: sn.pub/extras

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Preliminaries

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Shigeji Fujita, Kei Ito
      Pages 3-9

    3. Lattice Vibrations and Heat Capacity

      • Shigeji Fujita, Kei Ito
      Pages 11-24

    4. Free Electrons and Heat Capacity

      • Shigeji Fujita, Kei Ito
      Pages 25-42

    5. Electric Conduction and the Hall Effect

      • Shigeji Fujita, Kei Ito
      Pages 43-59

    6. Magnetic Susceptibility

      • Shigeji Fujita, Kei Ito
      Pages 61-73

    7. Boltzmann Equation Method

      • Shigeji Fujita, Kei Ito
      Pages 75-82

  3. Bloch Electron Dynamics

    1. Front Matter

      Pages 83-83
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    2. Bloch Theorem

      • Shigeji Fujita, Kei Ito
      Pages 85-95

    3. The Fermi Liquid Model

      • Shigeji Fujita, Kei Ito
      Pages 97-101

    4. The Fermi Surface

      • Shigeji Fujita, Kei Ito
      Pages 103-114

    5. Bloch Electron Dynamics

      • Shigeji Fujita, Kei Ito
      Pages 115-130

  4. Applications Fermionic Systems (Electrons)

    1. Front Matter

      Pages 131-131
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    2. De Haas–Van Alphen Oscillations

      • Shigeji Fujita, Kei Ito
      Pages 133-149

    3. Magnetoresistance

      • Shigeji Fujita, Kei Ito
      Pages 151-169

    4. Cyclotron Resonance

      • Shigeji Fujita, Kei Ito
      Pages 171-194

    5. Seebeck Coefficient (Thermopower)

      • Shigeji Fujita, Kei Ito
      Pages 195-204

    6. Infrared Hall Effect

      • Shigeji Fujita, Kei Ito
      Pages 205-215

  5. Back Matter

    Pages 221-244
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Physics, University at Buffalo, The State University of New York, Buffalo, USA

    Shigeji Fujita

  • Research Division, The National Center for University Entrance Examinations, Tokyo, Japan

    Kei Ito

About the authors

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.

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