Philip Taylor and Olle Heinonen. University of Cambridge Press, UK, 2002.
ISBN 0-521-77103-X
Reviewed by: A. H. Harker, Department of Physics and Astronomy, University College London, UK.
Published in Microscopy & Analysis, March 2003
Conventional text books on solid state physics tend to begin with geometrical descriptions and methods for analysing crystal structures. It is refreshing, then, to find that A Quantum Approach to Condensed Matter Physics acknowledges from the outset that most of the interesting properties of solids arise from excitations, and that the very first chapter introduces excitations such as phonons, solitons, magnons and plasmons.
The formal tone of the book is set in chapter 2, which introduces second quantisation in the context of the electron gas. This covers creation and annihilation operators and diagrammatic perturbation theory, and leads to the random phase approximation, the wavevector-dependent dielectric constant, and a simplified model of spin waves in a ferromagnetic electron gas. As everywhere in the book, the development is clear and the key points are well explained.
The title promises Condensed Matter rather than just Solid State Physics, and this is justified by the chapter on boson systems which gives a clear description of the Bogoliubov theory of liquid helium. The foundations laid here underpin the treatments of the BCS theory of superconductivity and of excitations in quantum Hall systems.
The chapter which comes closest to better-known texts on solid state physics is that on one-electron theory, which presents a fairly conventional treatment of electron states, the differences between insulators, semiconductors and metals, and electron dynamics in crystals. More advanced aspects such as the Green’s function method, relativistic effects and quasicrystals are touched upon, but very briefly. Density functional theory is reviewed, and a chapter is devoted to electron-phonon interactions.
The strictly quantum mechanical approach allows for the treatment of phenomena which are beyond the reach of many introductory texts. These include quantum point contact systems, including the Landauer Büttiker formalism and weak localisation effects. The quantum Hall effect is comprehensively covered, including the Laughlin ground state and excitations from it. There is one point here at which the cross-referencing in the book leaves something to be desired: collective excitations from the Laughlin ground state are compared with rotons in liquid helium, but the term ‘roton’ is not used in the chapter on liquid helium and does not appear in the index. The final chapter is a brief discussion of the Kondo effect and an introduction to heavy-Fermion physics.
The book contains exercises at the end of each chapter. Some are fairly straightforward problems that prove statements in the text such as ‘it takes but a tedious half-hour to show that….’, some prompt the reader to apply the ideas to interesting problems.
Although in principle one could approach this book armed only with a knowledge of quantum mechanics, it would be better to encounter it after an elementary course in condensed matter physics. This will provide a context for many of the phenomena that are covered here, and it is sometimes helpful to have the less formal descriptions from elementary texts in mind when interpreting the very mathematical treatment of the authors. Similarly, one needs to read beyond this book to appreciate the experimental measurements that the theory strives to explain. As an introduction to the modern theory of condensed matter, however, this book is excellent.