Misra Physics of Condensed Matter

1. Auflage 2011
ISBN: 978-0-12-384955-7
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 688 Seiten

Physics of Condensed Matter is designed for a two-semester graduate course on condensed matter physics for students in physics and materials science. While the book offers fundamental ideas and topic areas of condensed matter physics, it also includes many recent topics of interest on which graduate students may choose to do further research. The text can also be used as a one-semester course for advanced undergraduate majors in physics, materials science, solid state chemistry, and electrical engineering, because it offers a breadth of topics applicable to these majors. The book begins with a clear, coherent picture of simple models of solids and properties and progresses to more advanced properties and topics later in the book. It offers a comprehensive account of the modern topics in condensed matter physics by including introductory accounts of the areas of research in which intense research is underway. The book assumes a working knowledge of quantum mechanics, statistical mechanics, electricity and magnetism and Green's function formalism (for the second-semester curriculum). - Covers many advanced topics and recent developments in condensed matter physics which are not included in other texts and are hot areas: Spintronics, Heavy fermions, Metallic nanoclusters, Zno, Graphene and graphene-based electronic, Quantum hall effect, High temperature superdonductivity, Nanotechnology - Offers a diverse number of Experimental techniques clearly simplified - Features end of chapter problems

Autoren/Hrsg.

Misra, Prasanta

Inhaltsverzeichnis

1;Front Cover;1
2;Physics of Condensed Matter;4
3;Copyright;5
4;Dedication;6
5;Table of contents;8
6;Preface;22
6.1;Acknowledgments;24
7;Chapter 1. Basic Properties of Crystals;26
7.1;1.1 Crystal Lattices;27
7.2;1.2 Bravais Lattices in Two and Three Dimensions;29
7.3;1.3 Lattice Planes and Miller Indices;36
7.4;1.4 Bravais Lattices and Crystal Structures;38
7.5;1.5 Crystal Defects and Surface Effects;39
7.6;1.6 Some Simple Crystal Structures;40
7.7;1.7 Bragg Diffraction;44
7.8;1.8 Laue Method;45
7.9;1.9 Reciprocal Lattice;46
7.10;1.10 Brillouin Zones;52
7.11;1.11 Diffraction by a Crystal Lattice with a Basis;56
7.12;Problems;59
7.13;References;60
8;Chapter 2. Phonons and Lattice Vibrations;62
8.1;2.1 Lattice Dynamics;62
8.2;2.2 Lattice Specific Heat;73
8.3;2.3 Second Quantization;78
8.4;2.4 Quantization of Lattice Waves;86
8.5;Problems;91
8.6;References;93
9;Chapter 3. Free Electron Model;96
9.1;3.1 The Classical (Drude) Model of a Metal;96
9.2;3.2 Sommerfeld Model;98
9.3;3.3 Fermi Energy and the Chemical Potential;107
9.4;3.4 Specific Heat of the Electron Gas;109
9.5;3.5 DC Electrical Conductivity;111
9.6;3.6 The Hall Effect;112
9.7;3.7 Failures of the Free Electron Model;114
9.8;Problems;115
9.9;References;118
10;Chapter 4. Nearly Free Electron Model;120
10.1;4.1 Electrons in a Weak Periodic Potential;121
10.2;4.2 Bloch Functions and Bloch Theorem;124
10.3;4.3 Reduced, Repeated, and Extended Zone Schemes ;124
10.4;4.4 Band Index;126
10.5;4.5 Effective Hamiltonian;127
10.6;4.6 Proof of Bloch’s Theorem from Translational Symmetry;128
10.7;4.7 Approximate Solution Near a Zone Boundary;130
10.8;4.8 Different Zone Schemes;134
10.9;4.9 Elementary Band Theory of Solids;136
10.10;4.10 Metals, Insulators, and Semiconductors;137
10.11;4.11 Brillouin Zones;142
10.12;4.12 Fermi Surface;144
10.13;Problems;149
10.14;References;155
11;Chapter 5. Band-Structure Calculations;156
11.1;5.1 Introduction;156
11.2;5.2 Tight-Binding Approximation;156
11.3;5.3 LCAO Method;160
11.4;5.4 Wannier Functions;165
11.5;5.5 Cellular Method;167
11.6;5.6 Orthogonalized Plane-Wave (OPW) Method;170
11.7;5.7 Pseudopotentials;172
11.8;5.8 Muffin-Tin Potential;174
11.9;5.9 Augmented Plane-Wave (APW) Method;175
11.10;5.10 Green’s Function (KKR) Method;177
11.11;5.11 Model Pseudopotentials;181
11.12;5.12 Empirical Pseudopotentials;182
11.13;5.13 First-Principles Pseudopotentials;183
11.14;Problems;185
11.15;References;188
12;Chapter 6. Static and Transport Properties of Solids;190
12.1;6.1 Band Picture;191
12.2;6.2 Bond Picture;192
12.3;6.3 Diamond Structure;193
12.4;6.4 Si and Ge;193
12.5;6.5 Zinc-Blende Semiconductors;195
12.6;6.6 Ionic Solids;197
12.7;6.7 Molecular Crystals;199
12.8;6.8 Cohesion of Solids;199
12.9;6.9 The Semiclassical Model;204
12.10;6.10 Liouville’s Theorem;207
12.11;6.11 Boltzmann Equation;208
12.12;6.12 Relaxation Time Approximation;209
12.13;6.13 Electrical Conductivity;211
12.14;6.14 Thermal Conductivity;212
12.15;6.15 Weak Scattering Theory of Conductivity;213
12.16;6.16 Resistivity Due to Scattering by Phonons;217
12.17;Problems;219
12.18;References;221
13;Chapter 7. Electron–Electron Interaction;224
13.1;7.1 Introduction;224
13.2;7.2 Hartree Approximation;225
13.3;7.3 Hartree–Fock Approximation;228
13.4;7.4 Effect of Screening;232
13.5;7.5 Friedel Sum Rule and Oscillations;239
13.6;7.6 Frequency and Wave-Number-Dependent Dielectric Constant;242
13.7;7.7 Mott Transition;247
13.8;7.8 Density Functional Theory;248
13.9;7.9 Fermi Liquid Theory;250
13.10;7.10 Green’s Function Method;257
13.11;Problems;260
13.12;References;266
14;Chapter 8. Dynamics of Bloch Electrons;268
14.1;8.1 Semiclassical Model;268
14.2;8.2 Velocity Operator;269
14.3;8.3 k · p Perturbation Theory;270
14.4;8.4 Quasiclassical Dynamics;271
14.5;8.5 Effective Mass;272
14.6;8.6 Bloch Electrons in External Fields;273
14.7;8.7 Bloch Oscillations;279
14.8;8.8 Holes;280
14.9;8.9 Zener Breakdown (Approximate Method);283
14.10;8.10 Rigorous Calculation of Zener Tunneling;286
14.11;8.11 Electron–Phonon Interaction;289
14.12;Problems;296
14.13;References;299
15;Chapter 9. Semiconductors;300
15.1;9.1 Introduction;300
15.2;9.2 Electrons and Holes;303
15.3;9.3 Electron and Hole Densities in Equilibrium;304
15.4;9.4 Intrinsic Semiconductors;308
15.5;9.5 Extrinsic Semiconductors;309
15.6;9.6 Doped Semiconductors;310
15.7;9.7 Statistics of Impurity Levels in Thermal Equilibrium;313
15.8;9.8 Diluted Magnetic Semiconductors;315
15.9;9.9 Zinc Oxide;321
15.10;9.10 Amorphous Semiconductors;321
15.11;Problems;325
15.12;References;328
16;Chapter 10. Electronics;330
16.1;10.1 Introduction;330
16.2;10.2 p-n Junction;331
16.3;10.3 Rectification by a p-n Junction;336
16.4;10.4 Transistors;343
16.5;10.5 Integrated Circuits;350
16.6;10.6 Optoelectronic Devices;350
16.7;10.7 Graphene;354
16.8;10.8 Graphene-Based Electronics;357
16.9;Problems;358
16.10;References;361
17;Chapter 11. Spintronics;364
17.1;11.1 Introduction;364
17.2;11.2 Magnetoresistance;365
17.3;11.3 Giant Magnetoresistance;365
17.4;11.4 Mott’s Theory of Spin-Dependent Scattering of Electrons;367
17.5;11.5 Camley–Barnas Model;370
17.6;11.6 CPP-GMR;373
17.7;11.7 MTJ, TMR, and MRAM;377
17.8;11.8 Spin Transfer Torques and Magnetic Switching;381
17.9;11.9 Spintronics with Semiconductors;382
17.10;Problems;389
17.11;References;392
18;Chapter 12. Diamagnetism and Paramagnetism;394
18.1;12.1 Introduction;395
18.2;12.2 Atomic (or Ionic) Magnetic Susceptibilities;396
18.3;12.3 Magnetic Susceptibility of Free Electrons in Metals;403
18.4;12.4 Many-Body Theory of Magnetic Susceptibility of Bloch Electrons in Solids;413
18.5;12.5 Quantum Hall Effect;421
18.6;12.6 Fractional Quantum Hall Effect;425
18.7;Problems;426
18.8;References;432
19;Chapter 13. Magnetic Ordering;434
19.1;13.1 Introduction;435
19.2;13.2 Magnetic Dipole Moments;436
19.3;13.3 Models for Ferromagnetism and Antiferromagnetism;437
19.4;13.4 Ferromagnetism in Solids;447
19.5;13.5 Ferromagnetism in Transition Metals;452
19.6;13.6 Magnetization of Interacting Bloch Electrons;459
19.7;13.7 The Kondo Effect;464
19.8;13.8 Anderson Model;464
19.9;13.9 The Magnetic Phase Transition;465
19.10;Problems;468
19.11;References;473
20;Chapter 14. Superconductivity;476
20.1;14.1 Properties of Superconductors;477
20.2;14.2 Meissner–Ochsenfeld Effect;480
20.3;14.3 The London Equation;480
20.4;14.4 Ginzburg–Landau Theory;481
20.5;14.5 Flux Quantization;484
20.6;14.6 Josephson Effect;485
20.7;14.7 Microscopic Theory of Superconductivity;487
20.8;14.8 Strong-Coupling Theory;497
20.9;14.9 High-Temperature Superconductors;498
20.10;Problems;506
20.11;References;510
21;Chapter 15. Heavy Fermions;512
21.1;15.1 Introduction;513
21.2;15.2 Kondo-Lattice, Mixed-Valence, and Heavy Fermions;515
21.3;15.3 Mean-Field Theories;523
21.4;15.4 Fermi-Liquid Models;527
21.5;15.5 Metamagnetism in Heavy Fermions;531
21.6;15.6 Ce- and U-Based Superconducting Compounds;533
21.7;15.7 Other Heavy-Fermion Superconductors;538
21.8;15.8 Theories of Heavy-Fermion Superconductivity;541
21.9;15.9 Kondo Insulators;541
21.10;Problems;544
21.11;References;549
22;Chapter 16. Metallic Nanoclusters;552
22.1;16.1 Introduction;553
22.2;16.2 Electronic Shell Structure;556
22.3;16.3 Geometric Shell Structure;562
22.4;16.4 Cluster Growth on Surfaces;565
22.5;16.5 Structure of Isolated Clusters;567
22.6;16.6 Magnetism in Clusters;572
22.7;16.7 Superconducting State of Nanoclusters;583
22.8;Problems;587
22.9;References;590
23;Chapter 17. Complex Structures;592
23.1;17.1 Liquids;593
23.2;17.2 Superfluid 4He;595
23.3;17.3 Liquid 3He;598
23.4;17.4 Liquid Crystals;603
23.5;17.5 Quasicrystals;608
23.6;17.6 Amorphous Solids;615
23.7;Problems;619
23.8;References;622
24;Chapter 18. Novel Materials;624
24.1;18.1 Graphene;625
24.2;18.2 Fullerenes;633
24.3;18.3 Fullerenes and Tubules;638
24.4;18.4 Polymers;642
24.5;18.5 Solitons in Conducting Polymers;647
24.6;18.6 Photoinduced Electron Transfer;652
24.7;Problems;652
24.8;References;655
25;Appendix A: Elements of Group Theory;658
25.1;A.1 Symmetry and Its Consequences;658
25.2;A.2 Space Groups;659
25.3;A.3 Point Group Operations;661
25.4;Reference;664
26;Appendix B: Mossbauer Effect;666
26.1;B.1 Introduction;666
26.2;B.2 Recoilless Fraction;667
26.3;B.3 Average Transferred Energy;668
26.4;Reference;669
27;Appendix C: Introduction to Renormalization Group Approach;670
27.1;C.1 Critical Behavior;670
27.2;C.2 Theory for Scaling;671
27.3;C.3 Renormalization Group Approach;673
27.4;References;674
28;Index;676

Leseproben

Preface

This textbook is designed for a one-year (two semesters) graduate course on condensed matter physics for students in physics, materials science, solid state chemistry, and electrical engineering. It can also be used as a one-semester course for advanced undergraduate majors in physics, materials science, chemistry, and electrical engineering, and another one-semester course for graduate students in these areas. The book assumes a working knowledge of quantum mechanics, statistical mechanics, electricity and magnetism, and Green’s function formalism (for the second-semester curriculum). The book is written as a two-semester graduate-level textbook, but it can also be used as a reference book by faculty and other researchers actively engaged in research in condensed matter physics. With judicious choice of topics, the book can be divided into two parts: “Fundamental Concepts” designed to be taught in the first semester, and “Research Applications” to be taught in the second semester. Obviously, the first part can be taught to advanced undergraduate majors as an introductory course.

The later chapters are self-contained. Each research topic has a brief introduction, a review, and a summary of basic foundations for advanced research. This is done with the belief that the students will develop the skills and will be sufficiently prepared to develop an interest in one of the vast areas of the topics covered under the umbrella of “condensed matter physics.” In fact, this wide diversity of topics, the research on which has been increasing exponentially during the past decade, makes it nearly impossible to write a two-semester textbook for graduate students. Probably that is the reason for a dearth of graduate-level textbooks in condensed matter physics. This has led to an increasingly difficult task for the instructor because he or she has to prepare notes from a variety of textbooks, reference books, and review articles, especially to teach in the second-semester graduate level.

There has been slow but steady growth in the area of solid state physics after it was recognized as a separate branch of physics around 1940, probably after the publication of the book by Seitz. The main reason for this growth is solid state physics is essentially the applied branch of physics with a variety of technological applications and has attracted students from other disciplines. The slow but steady growth accelerated in the 1960s because of extensive research funding due to the space program, and eventually solid state physics became the major branch of physics attracting the maximum number of faculty and students. The American Physical Society officially changed the name of its largest group from “Solid State Physics” to “Condensed Matter Physics,” thereby including liquids and other soft materials. This change in 1978 has led to explosive growth in condensed matter physics during the past 30 years, and the material for supplementing the available textbooks has risen exponentially. In addition, research in various areas has accelerated rapidly, fueled by grants and a need for fast development in computer memory and storage as well as other applications of nanoscience and nanotechnology. The subject, which has now become multidisciplinary, includes materials science, solid state chemistry, and electrical engineering.

Recently, I wrote a book called , which is a part of the book series “Handbook of Metal Physics,” of which I am the series editor. A large number of distinguished physicists and chemists contributed to the book series and I have learned much while editing their work. These are advanced research?level books, but it became obvious that there is a need for a one-year (two-semester) graduate-level textbook in condensed matter physics that includes material on some of the new topics covered in this book series as well as in many other advanced research?level books and research reviews in prestigious journals. A graduate student should have the choice to select a topic for research after being taught in the classroom in order to acquire enough background on the topic. I have endeavored to do just that in this textbook, which has been limited to 18 chapters and 3 appendices. The project has taken several years, much longer than I had originally planned. I have learned a lot during this period, including the fact that the boundaries between the various disciplines in physics, chemistry, electrical engineering, and materials science are getting blurred.

The book has three objectives:

1. To present a coherent, clear, and intelligible picture of simple models of crystalline solids in the first few chapters. The properties of real solids, which are more complicated, are dealt with in later chapters. The more advanced topics are dealt with in the later part of each chapter (after the first few introductory chapters). Each chapter includes a collection of problems in order to enable students to have a grasp of the topics taught in the chapter. The problems at the end of each chapter are designed to make the students derive some of the formulas of analytical development with no intrinsic interest. The objective is to keep the book within a reasonable length, but more importantly, with the belief that the mathematical steps are better understood if they are derived by the students with the aid of hints and suggestions. In the second part of the book (Research Applications), some of the problems at the end of the chapter are extensions of the advanced topics covered in the chapter. In this part, some other problems are designed to make the applications of the topics more clear. It is up to the instructor to choose and assign the problems, and some instructors have their own list of problems. However, students should at least read all the problems even if they do not have any motivation or intention to solve them.

2. To present a comprehensive account of the modern topics in condensed matter physics by including introductory accounts of the areas where intense research is going on at present. To be able to do so, I have included chapters on Spintronics (Chapter 11), Heavy Fermions (Chapter 15), Metallic Nanoclusters (Chapter 16), and Novel Materials (Chapter 18). In addition, I have included sections on ZnO (Section 9.9), graphene (Section 10.7), graphene-based electronics (Section 10.8), quantum hall effect (Section 12.5), fractional quantum hall effect (Section 12.6), high-temperature superconductivity (Section 14.9), liquid 3He (Section 17.3), and quasicrystals (Section 17.5). Most of these topics are normally not included in standard textbooks in condensed matter physics. In fact, condensed matter physics is rapidly growing as an interdisciplinary subject because of its application in nanoscience and other areas of fast-growing science and technology. The objective of this book is to present the fundamental concepts as well as the methods for advanced research in this area.

3. To keep the size of the book within a reasonable length so that it can be taught as a two-semester course, I have avoided too many diagrams as well as excluded material not usually taught but included in most standard textbooks. I have also avoided including too many tables that list the properties of solids because these can be easily found in books specifically designed to provide such information. In addition, I have made a comprehensive review of many important topics such as band-structure calculations (Chapter 5), but left the details for students to learn if they are interested in doing research involving such topics.

I have consulted a large number of research papers and books while writing this textbook. It is not possible to acknowledge all these books and research papers at the appropriate places as is usually done in advanced research?level books. I have acknowledged whenever I have reprinted a figure with the permission of the author/publisher from a research paper published in a research journal or a book. I have also acknowledged at appropriate places whenever I have used any material published in research journals. There is a list of references at the end of each chapter where I have acknowledged the books and research papers I have used as primary sources of reference while writing this textbook.

Acknowledgments

I learned the skills to do research in theoretical solid state physics from Professor Laura M. Roth who was my Ph.D. advisor at Tufts University. I have improved those skills by working as a postdoctoral research associate with Professor Leonard Kleinman of the University of Texas at Austin. I learned a lot of basic techniques as well as gained physical insight to solve a variety of research problems during my 10 years of collaboration with late Professor Joseph Callaway of Louisiana State University. I am also thankful to Professor S. D. Mahanti of Michigan State University with whom I have collaborated and published several important research papers on applications of many-body theory. I am thankful to the distinguished physicists and chemists who have contributed to the book series “Hand Book of Metal Physics,” of which I had the privilege to be the Series Editor. I am thankful to the large number of colleagues and friends with whom I have consulted while writing this book, especially on their opinion as to what subjects should be included in a two-semester graduate-level textbook. I am also thankful to the graduate students who have worked on their Ph.D. theses under my...