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

Abstract

The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies k (T ). Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of QP peaks and appearance of sidebands, contained in the electron spectral function A(k, ω) = − mGR(k, ω)/π, where GR is the retarded Green's function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Fröhlich Hamiltonian by Mishchenko et al. (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fröhlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Fröhlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.

Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime inSrTiO3

“…The retarded cumulant approach includes higher-order e-ph Feynman diagrams beyond the Migdal approximation [37], and it produces accurate spectral functions (see below) that can capture the strong e-ph interactions. On the other hand, we have verified that the lowest-order Dyson-Migdal approximation generates spectral functions with large errors in the QP spectral weight and satellites energies, consistent with recent results at zero temperature [38].…”

Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators

“…For ionic insulators, the recent calculation of Lambrecht et al shows band-gap renormalizations up to 0.5 eV alone from Fröhlich electronphonon coupling [129]. Altogether, the electron-phonon coupling can lead to sizable ZPRs, for instance of over 1 eV for LiF [131]. In this work, we take into account the Fröhlich polaronic coupling for MgO, NaCl, LiCl, and LiF, using the results of Refs.…”

“…In this work, we take into account the Fröhlich polaronic coupling for MgO, NaCl, LiCl, and LiF, using the results of Refs. [129,131].…”

Phonon-induced renormalization of electron wave functions

“…The Allen-Heine-Cardona (AHC) theory [2][3][4] is one of the current state-of-the-art methods to study the effect of electron-phonon coupling (EPC) on electronic structures from first-principles density functional theory (DFT) and density functional perturbation theory (DFPT). Zero-point renormalization and temperature dependence of the electronic band gap [5][6][7][8][9][10][11][12][13] , optical responses [14][15][16] , and topological properties 17 are being actively investigated with the AHC theory.…”

“…More importantly, (ii) these methods are intrinsically adiabatic. Hence, they quantitatively or even qualitatively fail to predict the band gap renormalization of polar semiconductors 10,36 and cannot describe many-body effects such as the phonon satellites 11,37 .…”