Electron Phonon Interactions

In Chapter 8 we treated electrical transport. There we made the observation that one of the reasons why carriers scatter and lose momentum, is because they interact with the lattice vibrations, and this causes them to either gain or lose energy. Such processes, during which energy is exchanged, are called ‘inelastic scattering’ processes. But electron-lattice interactions do much more than just cause resistance. They are also at the origin of such phenomena as superconductivity where phonons help two electrons (fermions) to bind together to form bosons (integer spin particles) which can condense into superfluids. But we will not go as far as that in this book, and focus on some very elementary properties of electron-phonon coupling mainly the ones which enter transport properties.

Let us now look at the structure of the electron-lattice interaction, this coupling is also called the electron-phonon interaction. The reason for such a coupling, is that when atoms move around, vibrate and oscillate, they no longer form perfectly periodic arrays of potentials. But the electron Bloch functions were derived under the assumption that the system is at T = 0, and that the lattice is perfectly periodic. So these deviation from periodicity caused by thermal excitations cause a perturbation on the electron motion in Bloch bands, this causes them to scatter from one Bloch state k to another Bloch state k', exchanging momentum and energy in the process. The momentum difference is supplied by the lattice waves, or, in quantized form, by the ‘phonons’.