Polaron

Polaron is a quasiparticle consisting of a charge carrier, typically an electron or hole, together with the distortion of the surrounding lattice that the carrier induces by electron-phonon coupling. The coupling causes the carrier to become dressed by a cloud of lattice vibrations, modifying its energy, effective mass, and mobility. The concept helps explain charge transport in polar crystals, ionic solids, and some organic semiconductors where electron-phonon interactions are strong.

Polaron types are commonly distinguished by spatial extent and coupling strength. Large polarons, or Fröhlich polarons, arise when the lattice distortion extends over many lattice sites and the carrier remains relatively mobile; small polarons, or Holstein polarons, occur when the carrier becomes localized within a unit cell due to strong coupling or narrow electronic bandwidth, accompanied by a local distortion. Theories include continuum Fröhlich models for long-range coupling and lattice Holstein models for local coupling; the Lang-Firsov transformation and variational/path-integral methods are used to treat strong coupling, while perturbation theory applies at weak coupling.

Polaron properties include an increased effective mass and a polaron binding energy, and transport can switch from band-like to hopping-like as the polaron changes character. Temperature, crystal structure, and dielectric properties strongly influence mobility and optical response. Experimentally, polarons are inferred from signatures such as mid-infrared absorption, reduced mobility with temperature, and specific band renormalizations observed in spectroscopy and ARPES.

Polaron concepts apply across materials, including ionic and polar crystals, transition-metal oxides, perovskites, and organic semiconductors, where understanding electron-phonon coupling is essential for interpreting transport and optical behavior.