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We introduce a method that allows for the calculation of quasi-particle spectra in the GW approximation, yet avoiding any explicit reference to empty one-electron states. This is achieved by expressing the irreducible polarizability operator and the self-energy operator through a set of linear response equations, which are solved using a Lanczos-chain algorithm. We first validate our approach by calculating the vertical ionization energies of the benzene molecule and then show its potential by addressing the spectrum of a large molecule such as free-base tetraphenylporphyrin.
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We investigate the basic quantum mechanical processes behind non-proportional response of scintillators to incident radiation responsible for reduced resolution. For this purpose, we conduct a comparative first principles study of quasiparticle spectra on the basis of the $G_0W_0$ approximation as well as absorption spectra and excitonic properties by solving the Bethe-Salpeter equation for two important systems, NaI and SrI$_2$. The former is a standard scintillator material with well-documented non-proportionality while the latter has recently been found to exhibit a very proportional response. We predict band gaps for NaI and SrI$_2$ of 5.5 and 5.2 eV, respectively, in good agreement with experiment. Furthermore, we obtain binding energies for the groundstate excitons of 216 meV for NaI and 195$pm$25 meV for SrI$_2$. We analyze the degree of exciton anisotropy and spatial extent by means of a coarse-grained electron-hole pair-correlation function. Thereby, it is shown that the excitons in NaI differ strongly from those in SrI$_2$ in terms of structure and symmetry, even if their binding energies are similar. Furthermore, we show that quite unexpectedly the spatial extents of the highly anisotropic low-energy excitons in SrI$_2$ in fact exceed those in NaI by a factor of two to three in terms of the full width at half maxima of the electron-hole pair-correlation function.
The electronic band structure of SrTiO$_3$ is investigated in the all-electron QS$GW$ approximation. Unlike previous pseudopotential based QS$GW$ or single-shot $G_0W_0$ calculations, the gap is found to be significantly overestimated compared to experiment. After putting in a correction for the underestimate of the screening by the random phase approximation in terms of a 0.8$Sigma$ approach, the gap is still overestimated. The 0.8$Sigma$ approach is discussed and justified in terms of various recent literature results including electron-hole corrections. Adding a lattice polarization correction (LPC) in the ${bf q}rightarrow0$ limit for the screening of $W$, agreement with experiment is recovered. The LPC is alternatively estimated using a polaron model. We apply our approach to the cubic and tetragonal phases as well as a hypothetical layered post-perovskite structure and find that the LDA (local density approximation) to $GW$ gap correction is almost independent of structure.
Historically, the GW approach was put forward by Hedin as the simplest approximation to the so-called Hedin equations. In Section 2, we will derive these Hedin equations from a Feynman-diagrammatical point of view. Section 3.1 shows how GW arises as an approximation to the Hedin equations. In Section 3.2, we briefly present some typical GW results for materials, including quasiparticle renormalizations, lifetimes, and band gap enhancements. In Section 4, the combination of GW and DMFT is summarized. Finally, as a prospective outlook, ab initio dynamical vertex approximation D$Gamma$A is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.
With considering the great success of scanning tunnelling microscopy (STM) studies of graphene in the past few years, it is quite surprising to notice that there is still a fundamental contradiction about the reported tunnelling spectra of quasi-free-standing graphene monolayer. Many groups observed V-shape spectra with linearly vanishing density-of-state (DOS) at the Dirac point, whereas, the others reported spectra with a gap of 60 meV pinned to the Fermi level in the quasi-free-standing graphene monolayer. Here we systematically studied the two contradicted tunnelling spectra of the quasi-free-standing graphene monolayer on several different substrates and provided a consistent interpretation about the result. The gap in the spectra arises from the out-of-plane phonons in graphene, which mix the Dirac electrons at the Brillouin zone corners with the nearly free-electron states at the zone center. Our experiment indicated that interactions with substrates could effectively suppress effects of the out-of-plane phonons in graphene and enable us to detect only the DOS of the Dirac electrons in the spectra. We also show that it is possible to switch on and off the out-of-plane phonons of graphene at the nanoscale, i.e., the tunnelling spectra show switching between the two distinct features, through voltage pulses applied to the STM tip.
We introduce a new method for determining accurate values of the valence-band maximum in x-ray photoemission spectra. Specifically, we align the sharpest peak in the valence-band region of the experimental spectrum with the corresponding feature of a theoretical valence-band density of states curve from ab initio GW theory calculations. This method is particularly useful for soft and hard x-ray photoemission studies of materials with a mixture of valence-band characters, where strong matrix element effects can render standard methods for extracting the valence-band maximum unreliable. We apply our method to hydrogen-terminated boron-doped diamond, which is a promising substrate material for novel solar cell devices. By carrying out photoemission experiments with variable light polarizations, we verify the accuracy of our analysis and the general validity of the method.
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