Fully Anharmonic, Non-Perturbative First-Principles Theory of Electronic-Vibrational Coupling in Solids

The coupling between nuclear vibrations and the electronic structure plays a pivotal role for many material properties, including optical absorption and electronic transport. In this regard, however, todays state-of-the-art methodologies rely on two approximations [1]: the harmonic (phonon) approximation for the nuclear motion and the linear response description of the electronic structure with respect to harmonic displacements. In this work, we overcome both these approximations by performing fully anharmonic ab initio molecular dynamics (aiMD) calculations and by accounting for the non-perturbative, self-consistent response of the wavefunctions along the aiMD trajectory. By this means, we obtain fully anharmonic, vibronically renormalized spectral functions, from which macroscopic material properties like temperature-dependent band gaps and electronic transport coeffiecients are obtained. We validate our approach using silicon as an example, for which the traditional electron-phonon coupling formalism is recovered. Using cubic SrTiO₃ as example, we further demonstrate that anharmonic electronic-vibrational coupling effects not captured in traditional formalisms play a decisive role in complex materials like perovskites.
[1] F. Giustino, Rev. Mod. Phys. 89, 015003 (2017).