Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fröhlich polaron.

The electron-phonon interaction causes zero-point renormalization of electron quasiparticle (QP) energies ε_kn and broadening of QP peaks. Sidebands might also appear, as in the case of materials with infra-red active phonons. All these features are captured by the spectral function A(kn,ω)=-ImG_R(kn,ω)/π. Here we consider LiF and MgO and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the position and weight of both the QP peak and the sideband. Only one phonon satellite appears, with an unphysically large energy difference with respect to the QP peak. In contrast, a cumulant treatment [1],[2] gives an accurate QP energy and several satellites separated by the LO phonon energy. For the Fröhlich Hamiltonian, the positions of the QP peak and the first satellite agree closely with Monte Carlo results of Ref. [3]. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fröhlich Hamiltonian.

[1] D. Dunn, Can. J. Phys. 53, 321–337 (1975).
[2] C. Verdi et al., Nat. Comm. 8, 15769 (2017).
[3] A.S. Mishchenko et al., Phys. Rev. B 62, 6317 (2000).