Ziman Principles Of The Theory Of Solids 13 -

If an ion at position $\mathbfR$ displaces by $\mathbfu(\mathbfR, t)$ due to a phonon, the potential $V(\mathbfr)$ experienced by an electron at position $\mathbfr$ changes. The total potential is:

$$\delta E_c(\mathbfr) = E_1 , \nabla \cdot \mathbfu(\mathbfr)$$ ziman principles of the theory of solids 13

This simple scalar term is the workhorse for understanding scattering of electrons by acoustic phonons in simple metals and semiconductors. To make this quantitative, Chapter 13 introduces the second-quantized form of the interaction. Quantizing both the electron field and the phonon field, the interaction Hamiltonian becomes: If an ion at position $\mathbfR$ displaces by

This leads to a in the phonon dispersion curve $\omega(\mathbfq)$ at $\mathbfq = 2\mathbfk_F$. Experimentally observing Kohn anomalies (via neutron scattering) provides a direct measurement of the Fermi surface geometry—a powerful tool confirmed in metals like lead and niobium. 5. The Seed of Superconductivity (BCS Theory) No discussion of Chapter 13 is complete without its crowning achievement. While the chapter may stop short of full BCS theory, it lays the essential groundwork. Quantizing both the electron field and the phonon