Extending the Feynman polaron model for real materials

Most new semiconductors proposed for energy storage and transformation are soft and polar leading to a large dielectric electron-phonon coupling. This coupling drives the formation of polaron quasi particles, the electron dressed with phonon excitations.

The Feynman variational path-integral solution for the polaron problem[1] integrates out the infinite degrees of freedom of the phonon field, variationally matching the true electron-phonon Lagrangian to an integrable trial Lagrangian. This is an explicitly quasi-particle theory - the equations of motion for the trial Lagrangian are the same as an effective-mass electron coupled by a spring to a fictitious mass representing the phonon drag.

We implement this technique[1] in a modern code[2], taking material parameters from density functional and QS-GW electronic structure calculations. With this we have a quantum theory of temperature- and frequency-dependent mobility with no free parameters[3,4], and an ansatz for the nature of charge carriers in the material.

We will discuss: extending the Feynman theory to explicitly treat the multiple phonon branches present in complex, real, semiconductors; extending our codes to simulate the frequency dependent mobility; predicting the effect of polaron renormalisation on vibrational frequency and spectra; predicting Urbach tails from the instantaneous electric fields in a polar material; and show how charge-carrier scattering cross-sections are changed by the polaron localisation.