Fonons

Fonons, known in English as phonons, are quantized collective excitations of the periodic lattice of a crystal. They arise when the vibrational modes of the atoms are treated quantum mechanically as quantized normal modes. In a crystal with N atoms per primitive cell, there are 3N vibrational branches: three acoustic and 3N−3 optical. Phonons can be longitudinal or transverse and propagate with characteristic dispersion relations dependent on the wavevector within the Brillouin zone. Acoustic phonons correspond to in-phase motion of atoms and dominate low-energy vibrations; optical phonons correspond to out-of-phase motion and typically have higher energy.

Phonons interact with electrons, defects, and other phonons. They transport energy as heat and often determine a material’s thermal conductivity. They also couple to electrons, influencing electrical resistance and enabling conventional superconductivity through phonon-mediated electron pairing (BCS theory). Phonons contribute to a material’s heat capacity; at low temperatures, the Debye law predicts C ~ T^3, while at high temperatures the Dulong-Petit law applies. Scattering mechanisms such as boundary scattering, impurities, and Umklapp processes limit thermal conductivity.

Experimentally, phonons are observed via inelastic neutron scattering, Raman spectroscopy, and infrared spectroscopy. They play a central role in fields like thermoelectrics and phononics, where researchers tailor phonon spectra to control heat flow or thermal transport. In solid-state physics, phonons are a foundational concept for understanding lattice dynamics and a wide range of material properties.