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The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine- Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q G, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: a-A1N, β-A1N, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure. [ABSTRACT FROM AUTHOR]

The electron-phonon interaction plays a crucial role in many fields of physics and chemistry. Nevertheless, its actual calculation by means of modern many-body perturbation theory is weakened by the use of model Hamiltonians that are based on parameters difficult to extract from the experiments. Such shortcoming can be bypassed by using density-functional theory to evaluate the electron-phonon scattering amplitudes, phonon frequencies, and electronic bare energies. In this work, we discuss how a consistent many-body diagrammatic expansion can be constructed on top of density-functional theory. In that context, the role played by screening and self-consistency when all the components of the electron-nucleus and nucleus-nucleus interactions are taken into account, is paramount. A way to avoid overscreening is notably presented. Finally, we derive cancellation rules as well as internal consistency constraints in order to draw a clear, sound, and practical scheme to merge the many-body perturbation and density-functional theory. [ABSTRACT FROM AUTHOR]

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 nonperturbative 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. [ABSTRACT FROM AUTHOR]

The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g., density-functional theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak's theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janak's theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principles context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the density-functional perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion approximation. For the two different numerical approaches without non-rigid-ion terms, the agreement is better than 7 μeV in the case of diamond, which represent an agreement tof ive significant digits. The magnitude of the non-rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies. [ABSTRACT FROM AUTHOR]

We compute the zero-point renormalization (ZPR) of the optical band gap of diamond from many-body perturbation theory using the perturbative G0W0 approximation as well as quasiparticle self-consistent GW. The electron-phonon coupling energies are found to be more than 40% higher than standard density functional theory when many-body effects are included with the frozen-phonon calculations. A similar increase is observed for the zero-point renormalization in GaAs when G0W0 corrections are applied. We show that these many-body corrections are necessary to accurately predict the temperature dependence of the band gap. The frozen-phonon method also allows us to validate the rigid-ion approximation which is always present in density functional perturbation theory. [ABSTRACT FROM AUTHOR]

Highlights: [•] We verify the zero-point motion modification of the band gap between Abinit and QE/Yambo. [•] An agreement below 2meV between the two codes is obtained, converged toward 409meV. [•] We have sorted out the discrepancy in the literature. [•] We report an extensive convergence study (random/homogeneous wavevectors). [•] The influence of the pseudopotential choices is below 10%. [ABSTRACT FROM AUTHOR]