Electrons modified by phonons: Adiabatic versus non-adiabatic, and the persistence of electron quasiparticles

This talk will briefly review various types of renormalization of electron quasiparticles by phonons, including the question of when quasiparticle properties persist. Several new concerns will be discussed. In summary, band structure energies of order eV’s are affected by phonons of energy 100 times smaller. Semiconductor band gaps are altered by shifts of order 0.1 eV, and are temperature (T)-dependent. The component from thermal expansion is typically smaller than the renormalization from phonons. In metallic bands, an additional low T “mass renormalization”, m*/m>1 is observed. The ratio can range between 1.1 and 3.0. This is a non-adiabatic effect. At low T, metallic electrons notice the time-dependence of the vibrational displacements. The Eliashberg reformulation of conventional BCS superconductivity is closely related. The spectral functions of metallic electrons are often so broad that no recognizable quasiparticle peak is seen. Yet the quasiparticle picture functions nicely for understanding resistivity. Developments in computation have enabled good calculations of semiconductor band renormalization by phonons, which is mostly an adiabatic effect. Recently it has been realized that Froehlich polaron effects (and also piezo-polaron effects) need special treatment when computing energies of electrons close to the band gap. The (non-adiabatic) Froehlich polaron has a clear quasiparticle peak, plus phonon “satellites” in its spectral function. Surprisingly, the peak and satellites are badly misplaced in a conventional perturbative treatment. A “cumulant” version of the spectral function appears to solve the problem nicely. There are still aspects of phonon interactions with electrons that need reformulation, and remain challenges for theory and computation.