Solid State Physics

Here is the second Primer (forgive the oxymoron!) by Luciano Colombo, this time devoted to Solid State Physics. I reviewed about two years ago on this magazine (Il Nuovo Saggiatore, 36, N. 1-2 (2020)) his first excellent Primer on Atomic and Molecular Physics. My first statement of that review, “no good research without teaching, no good teaching without research”, applies even better to this textbook, in view of the fact that solid-state physics is the research area of Luciano Colombo. To be precise, he is a theoretical condensed-matter physicist with great experience in quantum molecular dynamics and first-principle quantum calculations, though with the good habit of closely communicating with the experimentalists. A productive attitude, resulting in excellent research and teaching at a time, and, of course, in a respectable number of highly praised textbooks (this is the fifth!) covering the structure of matter from atoms to solids (Elementi di Struttura della Materia, Hoepli 2002, and the first Primer), the theory of elasticity (Introduzione alla Teoria dell’Elasticità, coauthored with Stefano Giordano, Springer 2007) and the physics of semiconductors (Fisica dei Semiconduttori, Zanichelli, 2018).

This Primer, like the first one, has been designed for an undergraduate bachelor- level course and is organized in four parts: Preliminary concepts, the vibrational, thermal and elastic properties of solids, the electronic structure, and the concluding remarks on what is missing in this Primer and will consequently stimulate the students to next steps. The textbook is integrated by a rich series of nine appendices (35 pages) providing the accessory information for a more complete understanding of the various sections. Laurent Lewis (University of Montreal) in his beautiful preface argues that the title “solid state physics” sounds a bit out-of-date as compared to condensed-matter physics, but we have to convene that the chosen title is appropriate to a textbook where neither classical nor quantum liquids are mentioned.

The preliminary concepts take us in medias res providing first an overall picture (Chap. 1) where the atomistic model, presented in the previous Primer, serves as a basis to describe a solid-state system with its necessary approximations: the adiabatic approximation, the single-particle approximation for electrons, and the classical approach to the dynamics of ion cores.

This general introduction is followed by Chap. 2 providing the basic concepts on the periodic lattice structure of crystalline solids in the direct and reciprocal space, on the deviations from periodicity due to lattice defects, on the classification of solids according to the nature of interatomic bonding, and on the forces which hold solids together determining their cohesive energy. The second part of the textbook is devoted to the vibrational, thermal and elastic properties of solids. Chapter 3 introduces the reader to lattice dynamics, starting from the linear chains and then moving to the three-dimensional solids, including the diatomic ionic crystal, with a description of the LO-TO splitting. The quantization of the vibrational field leads to the concept of phonon and the experimental determination of the phonon dispersion relations by means of neutron inelastic scattering.

Thermal properties of solids (Chap. 4) are then fully understood in terms of phonon quanta, whereas the macroscopic elastic properties of crystalline solids (Chap. 5) are clearly exposed within the classical linear theory. The addition of an accurate discussion of thermo-elasticity (Sec. 5.4), not so frequent in solid-state physics textbooks, is an excellent idea. The electronic structure of solids is thoroughly treated in the third part of this Primer. After an introductory chapter exposing the general features of electrons in crystals, like the Fermi-Dirac distribution and the Bloch theorem (Chap. 6), the free electron theory for transport and optical properties in metals is exposed in the classical (Drude) and quantum (Sommerfeld) formulations (Chap. 7), clearly discussing their merits and failures. The failures call for the quantum band theory of electrons in periodic solids, beautifully presented in Chap. 8.

The application of band theory to semiconductors and their rich phenomenology (Chap. 9) is exposed in detail, in view of their fundamental and applicative importance. At the end of this part on electrons in solids, students will find a precious and very well written tutorial on density functional theory (DFT) (Chap. 10). Although based on a fundamental aspect of condensed-matter theory, the Hohenberg-Kohn theorem, DFT is generally not found in solid-state physics textbooks. Considering that first-principle calculations of the electronic structure have become daily bread in solid-state theory, I think the inclusion of DFT in a textbook is an excellent idea, an addition to the several merits of this Primer.

Giorgio Benedek
Università di Milano-Bicocca

Luciano Colombo

Solid State Physics

A primer

IOP Publishing Ltd, Bristol, 2021

pp. 310, $ 120,00

ISBN: 978-0-7503-2262-1

e-book: $ 95,00

ISBN: 978-0-7503-2265-2