Self-interaction in Green's-function theory of the hydrogen atom

Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation-theory (MBPT) in Hedin's GW approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the GW self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for GW and show that the self-interaction part of the GW self-energy, while non-zero, is small. The effect of calculating the GW self-energy from exact wavefunctions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating

Information criteria for nonlinear time series models

In this paper the performance of different information criteria for simultaneous model class and lag order selection is evaluated using simulation studies. We focus on the ability of the criteria to distinguish linear and nonlinear models. In the simulation studies, we consider three different versions of the commonly known criteria AIC, SIC and AICc. In addition, we also assess the performance of WIC and evaluate the impact of the error term variance estimator. Our results confirm the findings of different authors that AIC and AICc favor nonlinear over linear models, whereas weighted versions of WIC and all versions of SIC are able to successfully distinguish linear and nonlinear models. However, the discrimination between different nonlinear model classes is more difficult. Nevertheless, the lag order selection is reliable. In general, information criteria involving the unbiased error term variance estimator overfit less and should be preferred to using the usual ML estimator of the error term variance. © 2016 by De Gruyter

Band Bending Engineering at Organic/Inorganic Interfaces Using Organic Self-Assembled Monolayers

Adsorbing strong electron donors or acceptors on semiconducting surfaces induces band bending, whose extent and magnitude are strongly dependent on the doping concentration of the semiconductor. This study applies hybrid density-functional theory calculations together with the recently developed charge reservoir electrostatic sheet technique to account for charge transfer from the bulk of the semiconductor to the interface. This study further investigates the impact of surface-functionalization with specifically tailored self-assembled monolayers (SAMs). For the example of three chemically-similar SAMs, that all bond to the ZnO surface via pyridine docking groups, it is shown that the SAMs introduce shallow or deep donor levels that pin the band bending at the position of the SAM's highest occupied molecular orbital. In this way, the magnitude of the induced band bending can be controlled by the type of SAM, to a point where the doping-concentration dependence is completely eliminated

Electronic properties of lanthanide oxides from the GW perspective

A first-principles understanding of the electronic properties of f -electron systems is currently regarded as a great challenge in condensed-matter physics because of the difficulty in treating both localized and itinerant states on the same footing by the current theoretical approaches, most notably density-functional theory (DFT) in the local-density or generalized gradient approximation (LDA/GGA). Lanthanide sesquioxides (Ln2O3) are typical f -electron systems for which the highly localized f states play an important role in determining their chemical and physical properties. In this paper, we present a systematic investigation of the performance of many-body perturbation theory in the GW approach for the electronic structure of the whole Ln2O3 series. To overcome the major failure of LDA/GGA, the traditional starting point for GW, for f -electron systems, we base our GW calculations on Hubbard U corrected LDA calculations (LDA+U). The influence of the crystal structure, the magnetic ordering, and the existence of metastable states on the electronic band structures are studied at both the LDA+U and the GW level. The evolution of the band structure with increasing number of f electrons is shown to be the origin for the characteristic structure of the band gap across the lanthanide sesquioxide series. A comparison is then made to dynamical mean-field theory (DMFT) combined with LDA or hybrid functionals to elucidate the pros and cons of these different approaches

Exploring the random phase approximation: Application to CO adsorbed on Cu(111)

The adsorption of CO on the Cu(111) surface is investigated in the random phase approximation (RPA) as formulated within the adiabatic connection fluctuation-dissipation theorem. The RPA adsorption energy is obtained by adding a "local exchange-correlation correction" that is extrapolated from cluster calculations of increasing size, to the Perdew-Burke-Ernzerhof (PBE) value for the extended system. In comparison to density-functional theory calculations with the generalized gradient functionals PBE and AM05 and the hybrid functionals PBE0 and HSE03, we find a hierarchy of improved performance from AM05/PBE to PBE0/HSE03, and from PBE0/HSE03 to RPA, both in terms of the absolute adsorption energy as well as the adsorptionenergy difference between the atop and the hollow fcc sites. In particular, the very weak atop site preference at the PBE0/HSE03 level is further stabilized by about 0.2 eV in the RPA. The mechanism behind this improvement is analyzed in terms of the GW density of states that gives a spectral representation en par with the RPA formalism for the total energy

Vertex corrections in localized and extended systems

Within many-body perturbation theory we apply vertex corrections to various closed-shell atoms and to jellium, using a local approximation for the vertex consistent with starting the many-body perturbation theory from a DFT-LDA Green's function. The vertex appears in two places -- in the screened Coulomb interaction, W, and in the self-energy, \Sigma -- and we obtain a systematic discrimination of these two effects by turning the vertex in \Sigma on and off. We also make comparisons to standard GW results within the usual random-phase approximation (RPA), which omits the vertex from both. When a vertex is included for closed-shell atoms, both ground-state and excited-state properties demonstrate only limited improvements over standard GW. For jellium we observe marked improvement in the quasiparticle band width when the vertex is included only in W, whereas turning on the vertex in \Sigma leads to an unphysical quasiparticle dispersion and work function. A simple analysis suggests why implementation of the vertex only in W is a valid way to improve quasiparticle energy calculations, while the vertex in \Sigma is unphysical, and points the way to development of improved vertices for ab initio electronic structure calculations.Comment: 8 Pages, 6 Figures. Updated with quasiparticle neon results, extended conclusions and references section. Minor changes: Updated references, minor improvement

Controlling polarization at insulating surfaces: Quasiparticle calculations for molecules adsorbed on insulator films

By means of quasiparticle-energy calculations in the G0W0 approach, we show for the prototypical insulator-semiconductor system NaCl=Ge(001) that polarization effects at the interfaces noticeably affect the excitation spectrum of molecules adsorbed on the surface of the NaCl films. The magnitude of the effect can be controlled by varying the thickness of the film, offering new opportunities for tuning electronic excitations in, e.g., molecular electronics or quantum transport. Polarization effects are visible even for the excitation spectrum of the NaCl films themselves, which has important implications for the interpretation of surface science experiments for the characterization of insulator surfaces

Band gap and band parameters of InN and GaN from quasiparticle energy calculations based on exact-exchange density-functional theory

We have studied the electronic structure of InN and GaN employing G0W0 calculations based on exact-exchange density-functional theory. For InN our approach predicts a gap of 0.7 eV. Taking the Burnstein-Moss effect into account, the increase of the apparent quasiparticle gap with increasing electron concentration is in good agreement with the observed blue shift of the experimental optical absorption edge. Moreover, the concentration dependence of the effective mass, which results from the non-parabolicity of the conduction band, agrees well with recent experimental findings. Based on the quasiparticle band structure the parameter set for a 4x4 kp Hamiltonian has been derived.Comment: 3 pages including 3 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

GaN/AlN Quantum Dots for Single Qubit Emitters

We study theoretically the electronic properties of $c$-plane GaN/AlN quantum dots (QDs) with focus on their potential as sources of single polarized photons for future quantum communication systems. Within the framework of eight-band k.p theory we calculate the optical interband transitions of the QDs and their polarization properties. We show that an anisotropy of the QD confinement potential in the basal plane (e.g. QD elongation or strain anisotropy) leads to a pronounced linear polarization of the ground state and excited state transitions. An externally applied uniaxial stress can be used to either induce a linear polarization of the ground-state transition for emission of single polarized photons or even to compensate the polarization induced by the structural elongation.Comment: 6 pages, 9 figures. Accepted at Journal of Physics: Condensed Matte

New Perspective on Formation Energies and Energy Levels of Point Defects in Nonmetals

We propose a powerful scheme to accurately determine the formation energy and thermodynamic charge transition levels of point defects in nonmetals. Previously unknown correlations between defect properties and the valence-band width of the defect-free host material are identified allowing for a determination of the former via an accurate knowledge of the latter. These correlations are identified through a series of hybrid density-functional theory computations and an unbiased exploration of the parameter space that defines the Hyde-Scuseria-Ernzerhof family of hybrid functionals. The applicability of this paradigm is demonstrated for point defects in Si, Ge, ZnO, and ZrO2