Quantum Theory of Conducting Matter

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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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.

• Doping
• Fermi surface
• Helium-Atom-Streuung
• Quantum Hall effect
• Superconductor
• physics
• quantum mechanics
• quantum theory
• superconductivity

• 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

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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