ElectronPhonon

Electron-phonon interaction refers to the coupling between electrons and lattice vibrations in solids. Phonons are the quantized vibrational modes of a crystal, and electrons interact with these modes by scattering and by exchanging energy with lattice distortions. The coupling arises from mechanisms such as deformation-potential interaction with acoustic phonons and, in polar crystals, long-range Fröhlich coupling to optical phonons. The strength and spectrum of this interaction depend on crystal structure, electronic band dispersion, and screening.

In metals, electron-phonon scattering is a major source of electrical resistivity that increases with temperature. In conventional superconductors, the interaction provides the attractive mechanism that binds electrons into Cooper pairs; the coupling is retarded, allowing electron pairs to form despite Coulomb repulsion, as described by BCS theory and more thoroughly by Migdal-Eliashberg theory.

Quantitative descriptions use the electron-phonon spectral function α^2F(ω) and the dimensionless coupling constant λ, with λ = 2 ∫_0^∞ α^2F(ω)/ω dω. The superconducting critical temperature Tc and the quasiparticle self-energy are computed within Migdal-Eliashberg theory; empirical Tc formulas (McMillan, Allen-Dynes) relate Tc to λ and to the characteristic phonon frequency.

Ab initio methods such as density functional theory and density functional perturbation theory provide first-principles calculations of phonon spectra and electron-phonon matrix elements, enabling predictions of λ and α^2F(ω). Experimentally, ARPES, inelastic neutron scattering, Raman spectroscopy, and tunneling spectroscopy probe phonon modes and coupling strength and can be used to reconstruct α^2F(ω).

Electron-phonon coupling is central to conventional superconductivity and also influences thermal and transport properties in many metals and semiconductors, thermoelectrics, and some superconductors. It is an active area of materials design, where tailoring phonon spectra and coupling can optimize performance.