Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure

Abstract

The renormalization of the band structure at zero temperature due to electron-phonon coupling is explored in diamond, BN, LiF and MgO crystals. We implement a dynamical scheme to compute the frequency-dependent self-energy and the resulting quasiparticle electronic structure. Our calculations reveal the presence of a satellite band below the Fermi level of LiF and MgO. We show that the renormalization factor (Z), which is neglected in the adiabatic approximation, can reduce the zero-point renormalization (ZPR) by as much as 40%. Anharmonic effects in the renormalized eigenvalues at finite atomic displacements are explored with the frozen-phonon method. We use a non-perturbative expression for the ZPR, going beyond the Allen-Heine-Cardona theory. Our results indicate that high-order electron-phonon coupling terms contribute significantly to the zero-point renormalization for certain materials.PACS numbers: 63.20.kd, 63.20.dk, 71.15.Mb, 71.20.Nr The electron-phonon coupling is at the heart of numerous phenomena such as optical absorption 1,2 , thermoelectric transport 3 , and superconductivity 4-7 . It is also a crucial ingredient in basic electronic structure calculations, giving renormalized quasiparticle energies and lifetimes. This renormalization causes the temperature dependence of the band gap of semiconductors 8 , and accounts for the zero-point renormalization (ZPR), while the lifetime broadenings are observed through the electron mobility 9,10 and in photo-absorption/emission experiments 11 . Obtaining the quasiparticle structure from first principles has been a challenge, addressed for the first time for bulk silicon by King-Smith et al.12 , in 1989, using density functional theory (DFT), with a mixed frozen-phonon supercell and linear response approach. These authors pointed the inadequate convergence of their results with respect to phonon wavevector sampling, due to the limited available computing capabilities. Fifteen year passed, before Capaz et al. computed it for carbon nanotubes 13 using DFT with frozen phonons. At variance with the frozen-phonon approach, the theory of Allen, Heine and Cardona (AHC) [14][15][16] casts the renormalization and the broadening in terms of the first-order derivatives of the effective potential with respect to atomic positions. Used initially with empirical potentials, tight-binding or semi-empirical pseudopotentials 14-20 , AHC was then implemented with the density functional perturbation theory (DFPT) 21-24 , providing an efficient way to compute the phonon band structure and the electron-phonon coupling altogether. This powerful technique allowed A. Marini to compute, from first principles, temperature-dependent optical properties 25 . While DFPT has been widely applied to predict structural and thermodynamical properties of solids 26 , few * gabriel.antonius@gmail.com studies have used it to compute the phonon-induced renormalization of the band structure. The scarcity of experimental data is at least partly responsible for this imbalance. Whereas the phonon s...

Floquet analysis of excitations in materials

“…The best known example being the electron-phonon kinks in the ARPES spectrum of superconducting materials [85]. However, electron-phonon coupling is also known to result in observable distinct satellite, or shadow, bands in the photo-electron spectral function [86][87][88], also known as Polaron replicas [89][90][91][92][93]. The avenue to create a phonon-driven Floquet material is to selectively excite such strongly coupled phonon modes and thus to create new properties of the electronic structure or to better understand its properties, as for example realized in [94].…”

Precise effective masses from density functional perturbation theory

“…Provided that recent studies have exposed the substantial impact of electron-electron interactions on the calculated effective masses [5,8], it becomes interesting to investigate approximate schemes to include these interactions in the calculations. Furthermore, it would be interesting to investigate the impact of electron-phonon interaction not only on the band gap [37,[63][64][65][66][67][68][69], but also on the effective masses.…”

Ab initio Electronic Structure of Liquid Water

“…The inclusion of nuclear quantum effects (NQEs) noticeably modifies the structural and dynamical properties of liquid water [23][24][25][26][27][28][29]. In the context of the electronic structure, the quantum zero-point motion of nuclei renormalizes the electronic band gap [30][31][32][33][34][35][36][37][38][39]. As a consequence, quantum effects play an integral part in the description of the electronic structure of liquid water, but very often their importance is underappreciated in ab initio MD simulations.…”