Fononi

Fononi (singular fonone) are the quantized normal modes of vibrations in a crystal lattice, in physics commonly referred to as phonons in English. They arise in quantum treatments of lattice vibrations by promoting vibrational modes to quantum harmonic oscillators; each fonone carries energy E = h-bar omega and crystal momentum h-bar k. Fononi are bosons and obey Bose-Einstein statistics, enabling multiple fononi to occupy the same mode.

Fononi come in branches: acoustic fononi, whose frequency goes to zero as k -> 0, and optical fononi, which have finite frequency at k = 0 in crystals with more than one atom per primitive cell. In crystals with N atoms per primitive cell, there are 3N fononi branches: three acoustic and the remaining optical. Dispersion relations omega(k) describe their energy-momentum relation; long-wavelength acoustic fononi dominate heat capacity at very low temperatures with omega proportional to k; Debye model approximates this behavior; Einstein model treats optical modes as independent oscillators.

Fononi mediate thermal and electronic properties: they govern lattice thermal conductivity and contribute to specific heat; electron-phonon coupling gives electrical resistivity and, in conventional superconductors, the mechanism for Cooper pairing. Experimental probes include inelastic neutron scattering, Raman spectroscopy, and infrared absorption; fononi dispersion curves can be mapped in crystals by these methods.

Beyond bulk materials, nanostructures and interfaces modify fononi spectra, leading to fononi confinement and altered thermal transport. The term fononi is used in Italian literature to denote these quasi-particles, paralleling the English term phonons.