Solid-State Physics: Introduction to the Theory ,
How does one choose a text when teaching a graduate course in condensed-matter physics? Certainly for an undergraduate course, Charles Kittel’s Introduction to Solid State Physics (Wiley, 1953), whose eighth edition was published in 2005, comes immediately to mind. The many tables presented in the book were an indispensable resource to me, at least before the advent of Google. Neil Ashcroft and N. David Mermin’s Solid State Physics (Holt, Rinehart and Winston, 1976), which makes for more comfortable and leisurely reading than Kittel’s text, is an alternative. Neither text, however, would seem to have the depth needed for a graduate course. The remarkable early texts The Theory of the Properties of Metals and Alloys (Clarendon Press, 1936), by Nevill Mott and Harry Jones, and The Modern Theory of Solids (McGraw-Hill, 1940), by Frederick Seitz, are at a more appropriate level for a graduate course, but too much has happened in the past 70 years for either to serve as a modern text.
In the 1960s and 1970s, a flood of condensed-matter physics books appeared on the scene: Philip W. Anderson’s Concepts in Solids: Lectures on the Theory of Solids (W. A. Benjamin, 1963), John M. Ziman’s Principles of the Theory of Solids (Cambridge U. Press, 1964), my own Solid State Theory (McGraw-Hill, 1970), James Patterson’s Introduction to the Theory of Solid State Physics (Addison-Wesley, 1971), Ashcroft and Mermin’s text, and Otfried Madelung’s Introduction to Solid-State Theory (Springer-Verlag, 1978). The range of material and of approaches covered in the texts seems surprisingly similar. But years later, Harald Ibach and Hans Lüth’s Solid-State Physics: An Introduction to Theory and Experiment (Springer-Verlag, 1991) offered a distinctive approach. For most of us condensed-matter theorists, the first question asked when we consider a property is, “How do we estimate it?” But for Ibach and Lüth, the first question is, “How do we measure it?” That point of view suited my colleague Zhi-Xun Shen when we each taught part of a course at Stanford University: Shen used Ibach and Lüth’s text; I used my own. Even today, another distinctive possibility for a graduate text is Anderson’s book, because of the author’s unique insight. But the subjects covered are limited, with most of the content surprisingly centered on questions related to electronic-band structure.
Beyond the texts mentioned above, one faces a dazzling array of choices, including Solid-State Physics: Introduction to the Theory by Patterson and Bernard Bailey. An update to Patterson’s 1971 text, it adds a great deal of modern material, nearly doubling the size of the original. This expansion makes it definitely a candidate for a contemporary class. It was a prodigious task, as the authors indicate, to bring the book up to date. They included such developments as the Coulomb blockade, nanostructures, the quantum Hall effect, and fullerenes, all of which had not yet been discovered at the time of the first edition. The authors even went so far as to add in a model of the structure of white dwarfs and discuss crystal growth in space, although I found both subjects unsettling in their presentation. The discussion on the structure of white dwarfs is a jumble of equations, some of which, such as the relation between the volume of a sphere and its radius, are unnecessary. Others look wrong, such as equation 5.78, which is supposed to follow from equation 5.77; the error is presumably a misprint, but because so many factors are omitted, one cannot be sure. The section on crystal growth in microgravity, which I think has turned out to be the same as crystal growth in normal gravity, is an unbelievably convoluted explanation of why one who is in free fall does not feel gravity.
As the table of contents reveals, Patterson and Bailey’s book meets a requirement my colleague Volker Heine of Cambridge University once shared with me: He wanted a text to cover all the standard topics so that he could lecture only about the most interesting ones. When choosing a text, instructors should always check the contents first, then sample topics with which they are familiar to see how they are handled. Judging the topics covered may be subjective, but finding a text with which one is comfortable teaching is a subjective undertaking.
I found it instructive to try the approach on other texts first. For example, I looked at how several authors treated conduction in metals. Anderson asserts that “the only reason why an actual metal or semiconductor carries a current is the presence of relaxation effects.” True and perceptive, but seldom stated. Ziman writes that “the high conductivity of metals is to be ascribed to the high velocity of the few electrons at the top of the Fermi distribution, rather than to a high total density of free electrons which can be set slowly drifting.” Not true, but perhaps frequently thought. After deriving the conductivity, Madelung notes that “separating conductivity into charge, electron concentration, and mobility, the latter is seen to be µ = eτ(µ)/m*.” True, but not very informative. It seemed to me that each of those comments was characteristic of the book from which it came. After Patterson and Bailey derive the formula for conductivity, they assert that “equation (3.214) is a basic equation for the electrical conductivity. Again, (3.214) agrees with experiment more closely if m is replaced by a suitable m *.”
For my own taste, Patterson and Bailey’s book might prove problematic as a graduate text: It has too much algebra and too little physical insight. For example, the first analysis in chapter 1 is of the van der Waals force. That section takes up two pages of equations, qualifications, and assumptions when one clear paragraph would have sufficed. The next topic is Max Born’s theory of bonding in ionic crystals, but it is not done as nicely as the way Born had described it. That section offers a few introductory equations, including some irrelevant ones on thermodynamics and a table of cohesive energies in kilocalories per mole, so a physicist will have little idea of the physical magnitudes. And where are such modern insights as the realization that the energy per molecule required to separate the rock-salt crystal into neutral atoms is approximately equal to the difference in ionization potentials of the sodium and chlorine atoms? Too often the reader is left with many equations whose terms are incompletely defined and whose motivations are misleadingly described. The section on the Ginzburg–Landau equations seems to exemplify such cases. How the authors deal with that topic might prevent students from searching for a clear understanding of it, the kind of clarity that instructors hope to motivate their students with in class.
But, again, the choice of a text for a solid-state physics course, or any other physics-related course, is a personal one. The style of Patterson and Bailey’s Solid-State Physics might well fit that of some physics instructors.