Cumulant expansion treatment of phonon contributions to the electron spectral function

We present an approach for calculations of phonon contributions to the electron spectral function at finite temerature based on cumulant expansion techniques. Our approach is based on a many--pole representation of the Eliashberg function for the electron--phonon interaction, calculations of the dynamical matrix using ABINIT [1], and an Einstein self--energy model [2]. The code has been implemented as part of a plug--in to ABINIT for calculations of various phonon properties, and is applicable to complex structures with several atoms per unit cell. Results are given for a number of systems and compared to those obtained with the GW approximation.\\[4pt] [1] X. Gonze et al., Computational Materials Science \textbf{25}, 478 (2002). \\[0pt] [2] A. Eiguren and C. Ambrosch--Draxl, Phys. Rev. Lett. \textbf{101}, 036402 (2008).