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Register a new userThe GW plus cumulant method and plasmonic polarons: application to the homogeneous electron gas
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We study the spectral function of the homogeneous electron gas using many-body perturbation theory and the cumulant expansion. We compute the angle-resolved spectral function based on the GW approximation and the `GW plus cumulant approach. In agreement with previous studies, the GW spectral function exhibits a spurious plasmaron peak at energies 1.5$omega_{rm pl}$ below the quasiparticle peak, $omega_{rm pl}$ being the plasma energy. The GW plus cumulant approach, on the other hand, reduces significantly the intensity of the plasmon-induced spectral features and renormalizes their energy relative to the quasiparticle energy to $omega_{rm pl}$. Consistently with previous work on semiconductors, our results show that the HEG is characterized by the emergence of plasmonic polaron bands, that is, broadened replica of the quasiparticle bands, red-shifted by the plasmon energy.
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We apply a recently developed quasiparticle self-consistent $GW$ method (QSGW) to Gd, Er, EuN, GdN, ErAs, YbN and GdAs. We show that QSGW combines advantages separately found in conventional $GW$ and LDA+$U$ theory, in a simple and fully emph{ab initio} way. qsgw reproduces the experimental occupied $4f$ levels well, though unoccupied levels are systematically overestimated. Properties of the Fermi surface responsible for electronic properties are in good agreement with available experimental data. GdN is predicted to be very near a critical point of a first-order metal-insulator transition.
We have implemented the so called GW approximation (GWA) based on an all-electron full-potential Projector Augmented Wave (PAW) method. For the screening of the Coulomb interaction W we tested three different plasmon-pole dielectric function models, and showed that the accuracy of the quasiparticle energies is not sensitive to the the details of these models. We have then applied this new method to compute the quasiparticle band structure of some small, medium and large-band-gap semiconductors: Si, GaAs, AlAs, InP, SiMg$_2$, C and (insulator) LiCl. A special attention was devoted to the convergence of the self-energy with respect to both the {bf k}-points in the Brillouin zone and to the number of reciprocal space $bf G$-vectors. The most important result is that although the all-electron GWA improves considerably the quasiparticle band structure of semiconductors, it does not always provide the correct energy band gaps as originally claimed by GWA pseudopotential type of calculations. We argue that the decoupling between the valence and core electrons is a problem, and is some what hidden in a pseudopotential type of approach.
We describe an approach for calculations of phonon contributions to the electron spectral function, including both quasiparticle properties and satellites. The method is based on a cumulant expansion for the retarded one-electron Greens function and a many-pole model for the electron self-energy. The electron-phonon couplings are calculated from the Eliashberg functions, and the phonon density of states is obtained from a Lanczos representation of the phonon Greens function. Our calculations incorporate ab initio dynamical matrices and electron-phonon couplings from the density functional theory code ABINIT. Illustrative results are presented for several elemental metals and for Einstein and Debye models with a range of coupling constants. These are compared with experiment and other theoretical models. Estimates of corrections to Migdals theorem are obtained by comparing with leading order contributions to the self-energy, and are found to be significant only for large electron-phonon couplings at low temperatures.
A new implementation of the GW approximation (GWA) based on the all-electron Projector-Augmented-Wave method (PAW) is presented, where the screened Coulomb interaction is computed within the Random Phase Approximation (RPA) instead of the plasmon-pole model. Two different ways of computing the self-energy are reported. The method is used successfully to determine the quasiparticle energies of six semiconducting or insulating materials: Si, SiC, AlAs, InAs, NaH and KH. To illustrate the novelty of the method the real and imaginary part of the frequency-dependent self-energy together with the spectral function of silicon are computed. Finally, the GWA results are compared with other calculations, highlighting that all-electron GWA results can differ markedly from those based on pseudopotential approaches.
We present a new all-electron, augmented-wave implementation of the GW approximation using eigenfunctions generated by a recent variant of the full-potential LMTO method. The dynamically screened Coulomb interaction W is expanded in a mixed basis set which consists of two contributions, local atom-centered functions confined to muffin-tin spheres, and plane waves with the overlap to the local functions projected out. The former can include any of the core states; thus the core and valence states can be treated on an equal footing. Systematic studies of semiconductors and insulators show that the GW fundamental bandgaps consistently fall low in comparison to experiment, and also the quasiparticle levels differ significantly from other, approximate methods, in particular those that approximate the core with a pseudopotential.
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