Quantum Theory of Conducting Matter (eBook)

Newtonian Equations of Motion for a Bloch Electron

Shigeji Fujita, Kei Ito (Autoren)

eBook Download: PDF

2007 | 2007
XX, 244 Seiten
Springer New York (Verlag)
978-0-387-74103-1 (ISBN)

Infos

In a complex field, this work is a first. The authors make 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. They do this by deriving Newtonian equations of motion for the Bloch electron and diagonalizing the inverse mass (symmetric) tensor. The authors plan to follow up this book with a second, more advanced book on superconductivity and the Quantum Hall Effect.

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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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 "e;electron. "e; 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 "e;electrons"e; and the "e;holes"e; play important roles in conducting matter physics. The "e;electron"e; ("e;hole"e;), 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 "e;electrons"e; ("e;holes"e;) are generated, depending on the curvature sign of the Fermi s- face. The complicated Fermi surface of Ag can generate "e;electrons"e; and "e;holes,"e; and it is responsible for the observed negative Hall coe?cient R H and positive Seebeck coe?cient S.

Inhalt

Preface 5
Contents 8
Constants, Signs, Symbols, and General Remarks 12
Part I Preliminaries 19
Chapter 1 Introduction 20
1.1 Crystal Lattices 20
1.2 Theoretical Background 22
Chapter 2 Lattice Vibrations and Heat Capacity 27
2.1 Einstein’s Theory of Heat Capacity 27
2.2 Debye’s Theory of Heat Capacity 31
Chapter 3 Free Electrons and Heat Capacity 41
3.1 Free Electrons and the Fermi Energy 41
3.2 Density of States 46
3.3 Qualitative Discussions 52
3.4 Quantitative Calculations 54
Chapter 4 Electric Conduction and the Hall Effect 59
4.1 Ohm’s Law and Matthiessen’s Rule 59
4.2 Motion of a Charged Particle in Electromagnetic Fields 62
4.3 The Landau States and Levels 64
4.4 The Degeneracy of the Landau Levels 67
4.5 The Hall Effect: “Electrons” and “Holes” 72
Chapter 5 Magnetic Susceptibility 76
5.1 The Magnetogyric Ratio 76
5.2 Pauli Paramagnetism 79
5.3 Landau Diamagnetism 82
Chapter 6 Boltzmann Equation Method 89
6.1 The Boltzmann Equation 89
6.2 The Current Relaxation Rate 92
Part II Bloch Electron Dynamics 97
Chapter 7 Bloch Theorem 98
7.1 The Bloch Theorem 98
7.2 The Kronig–Penney Model 104
Chapter 8 The Fermi Liquid Model 109
8.1 The Self-consistent Field Approximation 109
8.2 Fermi Liquid Model 111
Chapter 9 The Fermi Surface 114
9.1 Monovalent Metals (Na, Cu) 114
9.2 Multivalent Metals 118
9.3 Electronic Heat Capacity and Density of States 122
Chapter 10 Bloch Electron Dynamics 126
10.1 Introduction 126
10.2 Newtonian Equations of Motion 128
10.3 Discussion 134
Part III Applications Fermionic Systems ( Electrons) 142
Chapter 11 De Haas– Van Alphen Oscillations 143
11.1 Onsager’s Formula 143
11.2 Statistical Mechanical Calculations: 3D 149
11.3 Statistical Mechanical Calculations: 2D 152
11.4 Two-Dimensional Conductors 157
Chapter 12 Magnetoresistance 160
12.1 Introduction 160
12.2 Anisotropic Magnetoresistance in Cu 162
12.3 Shubnikov–De Haas Oscillations 164
12.4 Heterojunction GaAs/AlGaAs 170
Chapter 13 Cyclotron Resonance 179
13.1 Introduction 179
13.2 Cyclotron Resonance in Ge and Si 180
13.3 Cyclotron Resonance in Al 192
13.4 Cyclotron Resonance in Pb 196
13.5 Cyclotron Resonance in Zn and Cd ( HCP) 200
Chapter 14 Seebeck Coefficient ( Thermopower) 203
14.1 Introduction 203
14.2 Quantum Theory 205
14.3 Discussion 208
Chapter 15 Infrared Hall Effect 213
15.1 Introduction 213
15.2 Kinetic Theory 217
15.3 Discussion 221
Appendix A Electromagnetic Potentials 224
Appendix B Statistical Weight for the Landau States 228
B.1 The Three-Dimensional Case 228
B.2 The Two-Dimensional Case 230
Appendix C Derivation of Equation (11.19) 231
References 232
Chapter 1 232
Chapter 2 232
Chapter 3 232
Chapter 4 232
Chapter 5 232
Chapter 7 233
Chapter 8 233
Chapter 9 233
Chapter 10 233
Chapter 11 234
Chapter 12 234
Chapter 13 235
Chapter 14 235
Chapter 15 236
Appendix B 236
Appendix C 236
Bibliography 237
Solid State Physics 237
Background 237
Index 240

Produkt-Details

• Erscheint lt. Verlag: 30.11.2007
• Zusatzinfo: XX, 244 p. 80 illus.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik
• Schlagworte: Doping • Fermi surface • Helium-Atom-Streuung • Physics • Quantum Hall Effect • quantum mechanics • Quantum Theory • Superconductivity • Superconductor
• ISBN-10: 0-387-74103-8 / 0387741038
• ISBN-13: 978-0-387-74103-1 / 9780387741031