Phonons, photons, and electrons

Abstract

When the sky is illumined with crystal Then gladden my road and broaden my path And clothe me in light. From “The Book of the Dead,” Ancient Egypt Translated by Robert Hillyer In this chapter we turn to phonons, photons, and their interactions with electrons. These interactions play an important role in condensed matter physics. At room temperature, the resistivity of metals results mainly from electron–phonon interaction. At low temperature, this interaction is responsible for the superconducting properties of many metals. On the other hand, the electron–photon interaction plays a dominant role in light scattering by solids, from which we derive a great deal of information about excitation modes in solids. Much of our knowledge about energy bands in crystals has been obtained through optical absorption experiments, whose interpretation relies on an understanding of how electrons and photons interact. We begin by discussing lattice vibrations in crystals and show that, upon quantization, the vibrational modes are described in terms of phonons, which are particle-like excitations that carry energy and momentum. We will see that the effect of lattice vibrations on electronic states is to cause scattering, whereby electrons change their states by emitting or absorbing phonons. Similarly, the interaction of electrons with an electromagnetic field will be represented as scattering processes in which electrons emit or absorb photons.