Band Theory and Electronic Properties of Solids , John Singleton Oxford U. Press, New York, 2001. $70.00, $35.00 paper (222 pp.). ISBN 0-19-850645-7, ISBN 0-19-850644-9 paper
As the field of condensed matter physics grows, finding the perfect text for an advanced undergraduate or beginning graduate course becomes more and more difficult. To cover the fundamental principles in any kind of comprehensive, rigorous fashion is already a vast undertaking. To keep the work up to date and to convey a sense of the exciting possibilities offered by current research in the field requires a breadth of knowledge possessed by a rare few. If then are added the pedagogical requirements—that the text be easy to follow for most students and that it provide ample instructive exercises—the magnitude of the problem becomes obvious.
The Oxford Master Series in Condensed Matter Physics offers an appealing alternative to conventional texts: a set of slim volumes, each on a separate topic and complete with exercises, written by active researchers who can combine a current perspective with the presentation of the relevant fundamental principles. Band Theory and Electronic Properties of Solids , by Oxford University physicist John Singleton, fits into the Oxford series between an upcoming volume on structure and dynamics and existing volumes on optical properties, magnetism, superconductivity, and soft condensed matter physics.
The focus of this particular volume is considerably narrower than the title suggests. The pedagogical strategy is to present the electronic properties of solids within the semiclassical theory of electronic transport. At that level, electronic properties depend only on bandstructure features and thus are largely independent of other details and complexities. For metals, the salient features include the effective dimensionality and density of states at the Fermi level, and topology of the Fermi surface. The analogous quantities for semiconductors are the gap and the effective masses. The semiclassical framework has the advantage of rendering the electronic properties of currently interesting systems (organic molecular solids, manganite oxides, and semiconductor superlattices) as accessible as those of the classic examples of copper and lithium. Sections that describe modern experimental techniques, particularly Fermi-surface determination, complement the theoretical discussion.
This clear-cut agenda is a definite strength of the book, but much is missing, and readers will have to adjust their expectations. There is virtually nothing about band theory per se—that is, how the details of bands in a specific material are related to that material’s composition and crystal structure. Nor does anything appear about modern methods for performing the relevant computations or about symmetry beyond lattice periodicity. The puzzles of the success of the one-electron approximation and of the nearly-free-electron approximation are hardly addressed, and there is no systematic explanation of the semiclassical approximation itself or the conditions for its breakdown. Electronic properties other than electrical and thermal conductivity are not covered.
The warm informality of the style makes readers feel as if they were attending the lectures. Neil Ashcroft and David Mermin’s Solid State Physics (Holt, Rinehart and Winston, 1976) receives extensive homage, not only through numerous page references for more rigorous treatments but also through the copious use of footnotes and the sprinkling of humorous items through the index.
The level of presentation is quite qualitative. Technical terms and phrases, such as bandstructure engineering, spin density wave, and variable range hopping, appear in boldface. In many instances, verbal and pictorial descriptions replace equations. For some topics, this approach works well, the chapters on magnetoresistance being particularly successful. For other topics, oversimplification makes it harder, not easier, for readers to understand the concept.
Because of its origin as a course in the Oxford University physics curriculum, this book will not easily lend itself as the main text for a course in an American university. Although the book assumes some previous knowledge of solid-state physics (recapped in a series of appendices to make the book more self-contained) the discussion assumes only a passing acquaintance with quantum mechanics. For most advanced undergraduate physics majors, the reverse is more typical.
For a graduate course, the deemphasis of quantum mechanics is even more problematic. Moreover, the level of presentation is too qualitative for the book to be used on its own. However, as a supplementary text for students (and there are many of them) who find it heavy going to study higher-level texts such as Ashcroft and Mermin, or the more recent excellent monograph Solid State Physics by Giuseppe Grosso and Giuseppe Pastori Parravicini (Academic Press, 2000), this book is highly recommended. Its readable and enjoyable format will help students to develop an intuition for electronic properties.
