Having time to read was one of the few perks of feeling ill over the Christmas holidays. I had a chance to finish the 1964 classic text by J. M. Ziman, Principles of the Theory of Solids. He writes with a certain eloquence and authority that you don’t often find in physical science. It is not a text for true beginners, but addresses many fundamental concepts in condensed-matter physics with a unique perspective and a clear narrative.
A few choice quotes to stimulate the mind:
Lattice periodicity and k-points: “There are exactly as many allowed wave-vectors in a Brillouin zone as there are unit cells in a block of crystal.”
Electrostatic summations of ionic solids: “The problem of computing such a sum becomes very serious. The best direct method is that of Evjen, where one treats successive shells, going outward from the origin, each one being exactly neutral in charge.”
Special points in an electronic band structure: “For a given amount of computing, we can get more accurate values of E(k) at points of high symmetry, than we can at an arbitrary point in the [Brillouin] zone.”
Ionic semiconductors: “It is doubtful whether a hole can move like a free particle in an ionic crystal. The small overlap between valence orbitals on neighbouring ions implies a very narrow valence band with a correspondingly high effective mass.”
Carrier mobility in semiconductors: “The scattering of carriers by lattice vibrations in semiconductors is, in general, a much simpler problem. Because the carriers are usually thought of as concentrated in a small region of k-space, near a minimum in E(k), the possible change of k-vector in the scattering is small.”
Ising model: “The importance of the Ising model is not, however, in the description of particular physics effects; it is a mathematically tractable model of a system that should exhibit co-operative phenomena and phase transitions.”