Über die Autorin bzw. den Autor

Gerald D. Mahan is Distinguished Professor of Physics at Pennsylvania State University. His books include Quantum Mechanics in a Nutshell (Princeton) and Many-Particle Physics.

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"Mahan's book does an admirable job of covering the broad subject of condensed matter physics in a balanced way. Virtually every important modern topic is explained. The informal narrative style gives the reader the sense of sitting in on a lecture by the master. The long search for a suitable text for a one-year graduate course on condensed matter physics may finally be over."--Patrick A. Lee, Massachusetts Institute of Technology

"This book is a great place to start learning about the vast array of phenomena that nature is able to produce around us in the form of materials. It hardly fits in a nutshell--it covers a great many topics, both traditional and current, in condensed matter physics. It is more akin to Hamlet's assertion that he could be bounded in a nutshell, and count himself a king of infinite space. The prodigious knowledge of the author shines through in the choice of topics."--Sidney R. Nagel, University of Chicago

"This is an excellent book that shows the author's wide grasp of the material. I particularly appreciate the many problems at the end of each chapter. Another welcome feature is the inclusion of many hot, still-developing topics in contemporary solid state physics."--Torgny Gustafsson, Rutgers University

"Mahan is a nuts-and-bolts theorist. Condensed Matter in a Nutshell includes many current hot topics, and the problem sets are well chosen. The book will help those trained in chemistry and materials science, both professionals and students, to come to grips with the current thinking in condensed matter physics, and it directs readers where to go for deeper immersion."--Zachary Fisk, University of California, Irvine

Aus dem Klappentext

"Mahan's book does an admirable job of covering the broad subject of condensed matter physics in a balanced way. Virtually every important modern topic is explained. The informal narrative style gives the reader the sense of sitting in on a lecture by the master. The long search for a suitable text for a one-year graduate course on condensed matter physics may finally be over."--Patrick A. Lee, Massachusetts Institute of Technology

"This book is a great place to start learning about the vast array of phenomena that nature is able to produce around us in the form of materials. It hardly fits in a nutshell--it covers a great many topics, both traditional and current, in condensed matter physics. It is more akin to Hamlet's assertion that he could be bounded in a nutshell, and count himself a king of infinite space. The prodigious knowledge of the author shines through in the choice of topics."--Sidney R. Nagel, University of Chicago

"This is an excellent book that shows the author's wide grasp of the material. I particularly appreciate the many problems at the end of each chapter. Another welcome feature is the inclusion of many hot, still-developing topics in contemporary solid state physics."--Torgny Gustafsson, Rutgers University

"Mahan is a nuts-and-bolts theorist. Condensed Matter in a Nutshell includes many current hot topics, and the problem sets are well chosen. The book will help those trained in chemistry and materials science, both professionals and students, to come to grips with the current thinking in condensed matter physics, and it directs readers where to go for deeper immersion."--Zachary Fisk, University of California, Irvine

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Condensed Matter in a Nutshell

PRINCETON UNIVERSITY PRESS

Contents

Preface....................................................xiii1 Introduction.............................................12 Crystal Structures.......................................93 Energy Bands.............................................314 Insulators...............................................685 Free Electron Metals.....................................946 Electron–Electron Interactions.....................1277 Phonons..................................................1768 Boson Systems............................................2309 Electron–Phonon Interactions.......................25410 Extrinsic Semiconductors................................28711 Transport Phenomena.....................................32012 Optical Properties......................................37913 Magnetism...............................................41814 Superconductivity.......................................46715 Nanometer Physics.......................................511Appendix...................................................541Index......................................................553

Chapter One

The history of material science is closely tied to the availablility of materials. Experiments must be done on samples. In the early days of the twentieth century, most of the available materials were found in nature. They were minerals or compounds.

1.1 1900–1910

Scanning the table of contents of the Physical Review for the decade 1900–1910, one finds that experiments were done on the following elements and compounds:

• Alkali metals: Na, K, Rb

• Noble metals: Cu, Ag, Au

• Divalent metals: Zn, Cd

• Multivalent metals: Al, Sn, Hg, Bi, Pb

• Transition metals: Ti, Fe, Ni, Mo, Rh, Ta, W, Ir, Pt

• Rare earth metals: Er

• Semiconductors: C, Si, Se, P

• Binary compounds: CaO, MgO, ZnS, HgS, CdS, H2O, AgCl, AgBr, NaF, NaBr, NaCl, LiCl, KCl, TlCl, TlBr, PbCl2, PbCl2, PbI2

• Oxides: KNO3, LiNO3, NaNO3, AgNO3, K2Cr2O2, NaClO3

The binary compounds were identified by their chemical name, such as cadmium sulfide, calcium oxide, or ice.

Among the most interesting materials were minerals. They were usually, and often only, identified by their mineral name. A partial list is given in table 1.1. Several minerals we were unable to identify from their names. The point of this list is that all of these compounds are found in nature as crystals. The samples were not grown in the laboratory, they were found in caves or mines. ZnS was then called sidot blende, but today is called zincblende.

A few materials were actually grown in a laboratory. One was silicon, which was grown in the research laboratory of the General Electric Company. Other artificial materials used in experiments were rubber, brass, asphalt, steel, constantan, and carborundum.

1.2 Crystal Growth

Today nearly all materials used in experiments are either grown in a laboratory or purchased from a company that grew them in a laboratory. The techniques were discovered one by one during the twentieth century. Some notable landmarks:

1. Jan Czochralski invented a method of pulling crystals from their melt in 1917. His apparatus is shown in fig. 1.1. The crystals are pulled vertically, slowly, starting with a small seed crystal. Today the crystal is rotated to ensure that inhomogenieties in the liquid do not make the crystals inhomogeneous. Two-thirds of crystals are grown using the Czochralski method. Large single crystals are prepared this way. For example, silicon crystals used in the manufacturing of integrated circuits are pulled.

2. Percy Bridgman reported the Bridgman method in 1925. A hollow cylinder is packed with powder or small crystals. It is pulled slowly through a hot region, where the material is melted and recrystalized. Large single crystals can be made this way. The cylinder can be moved vertically or horizontally.

3. William Pfann invented the method of zone refining in 1952, whereby a crystal is pulled through a hot area that locally melts and recrystallizes it. Zone refining generally purifies a crystal, by pushing impurities to the end of the crystal. A crystal may be zone refined several times to obtain a low density of impurities.

4. Large single crystals may be grown from a melt. A supersturated solution of the compound will precipitate the excess material. At the right temperature, it precipitates by growing single crystals. This process happens daily in the author's pantry, as large sugar crystals are grown in the container of maple syrup. This rock candy is a family favorite.

5. Small crystals can be grown in a vapor. The material is inserted into a container, often a glass tube. Then it is heated, so the vapor is supersaturated. At the right temperature, it will grow crystals. This process is slow, but is used for laboratory samples.

The above methods are all traditional, and make three-dimensional, homogeneous samples. Many crystals today are grown using epitaxy. Epitaxy is the technique of growing a crystal, layer by layer, on the atomically flat surface of the same, or another, crystal. The atoms are brought to the surface by a variety of methods.

• Molecular beam epitaxy (MBE) uses a beam of atoms, or molecules, that are directed toward the surface. John Arthur reported this method in 1968 for growing layers of GaAs. The particle beams originate in a small furnace that creates a vapor of the material, and a hole in the furnace lets atoms out. This process is very slow, but is widely practiced.

• Chemical vapor deposition (CVD) uses a vapor of the material in contact with the surface. This method is also called vapor-phase epitaxy (VPE).

• Liquid phase epitaxy (LPE) has a liquid of the material in contact with the surface. It is a variation of the solution method mentioned earlier.

1.3 Materials by Design

There are about 92~100 stable elements in the periodic table. Around 10⁴ binary compounds can be formed from pairs of different atoms. Not all pairs form a compound, but many pairs form several different crystals. Putting three elements together has about 10⁶ possible compounds, and putting four elements together has about 10⁸ possible compounds. The number of new materials that are grown for the first time is thousands each year. Most of these new compounds have rather ordinary properties. However, occasionally one is found that is a high-temperature superconductor, a high-field magnet, or an excellent thermoelectric. Condensed matter physics continues to be an exciting area of research, because new crystals are constantly being discovered. There seems to be no end to this process, since the number of possible new compounds is endless.

An interesting challenge is to try to make this process more efficient. At the moment the scientific community grows thousands of new materials, and a few turn out to be interesting. This process is obviously inefficient. I challenge you, the reader, to find the answer to the following questions:

• What material is the best superconductor? It would have the highest transition temperature T_c to the superconducting phase. Do not tell me the electronic properties or the best density of states. Tell me which atoms are in the crystal, and in what arrangement....