Question

Explain why phonon dispersion only can be expressed in the first Brillouin zone, but the electron band structure can be extended to second or third Brillouin zone. (Please briefly description)

Answer 1

Phonons are the basis of our understanding of the thermal properties of insulators; such as specific heat & thermal conductivity. In metals however, there are electronic contributions as well.They are basically the quanta of elastic waves in the solid. Compare with photons being the quanta of EM radiation. Acoustic phonons at long wavelengths are sound waves.At finite temperatures, the atoms of the crystal vibrate due to their thermal energy. We can treat such vibrations classically (as a set of harmonic oscillators), or quantum mechanically (as a phonon gas - like we did the photon gas & blackbody radiation). Quantum effects are always important for phonons, except at high temperatures.

(IN IMAGE)Looking at the repeated zone representation, it can be concluded that the region in the first Brillouin zone, between and , contains all of the information in a compact manner. Therefore it is often considered sufficient to show all of the allowed wave vectors and energy levels within the first Brillouin zone itself. Such a representation is referred to as the „Reduced zone‟ representation.