GW approximation with self-screening correction

The \emph{GW} approximation takes into account electrostatic self-interaction contained in the Hartree potential through the exchange potential. However, it has been known for a long time that the approximation contains self-screening error as evident in the case of the hydrogen atom. When applied to the hydrogen atom, the \emph{GW} approximation does not yield the exact result for the electron removal spectra because of the presence of self-screening: the hole left behind is erroneously screened by the only electron in the system which is no longer present. We present a scheme to take into account self-screening and show that the removal of self-screening is equivalent to including exchange diagrams, as far as self-screening is concerned. The scheme is tested on a model hydrogen dimer and it is shown that the scheme yields the exact result to second order in $(U_{0}-U_{1})/2t$ where $U_{0}$ and $U_{1}$ are respectively the onsite and offsite Hubbard interaction parameters and $t$ the hopping parameter.Comment: 9 pages, 2 figures; Submitted to Phys. Rev.

Dielectric screening in extended systems using the self-consistent Sternheimer equation and localized basis sets

We develop a first-principles computational method for investigating the dielectric screening in extended systems using the self-consistent Sternheimer equation and localized non-orthogonal basis sets. Our approach does not require the explicit calculation of unoccupied electronic states, only uses two-center integrals, and has a theoretical scaling of order O(N^3). We demonstrate this method by comparing our calculations for silicon, germanium, diamond, and LiCl with reference planewaves calculations. We show that accuracy comparable to planewaves calculations can be achieved via a systematic optimization of the basis set.Comment: 6 pages, 3 figure

Simulation of neutrino and charged particle production and propagation in the atmosphere

A precise evaluation of the secondary particle production and propagation in the atmosphere is very important for the atmospheric neutrino oscillation studies. The issue is addressed with the extension of a previously developed full 3-Dimensional Monte-Carlo simulation of particle generation and transport in the atmosphere, to compute the flux of secondary protons, muons and neutrinos. Recent balloon borne experiments have performed a set of accurate flux measurements for different particle species at different altitudes in the atmosphere, which can be used to test the calculations for the atmospheric neutrino production, and constrain the underlying hadronic models. The simulation results are reported and compared with the latest flux measurements. It is shown that the level of precision reached by these experiments could be used to constrain the nuclear models used in the simulation. The implication of these results for the atmospheric neutrino flux calculation are discussed.Comment: 11 pages, 9 figure

Influence of pressure and temperature on key physicochemical properties of corn stover-derived biochar

This study focuses on analyzing the effect of both the peak temperature and pressure on the properties of biochar produced through slow pyrolysis of corn stover, which is a common agricultural waste that currently has little or no value. The pyrolysis experiments were carried out in a fixed-bed reactor at different peak temperatures (400, 525 and 650 °C) and absolute pressures (0.1, 0.85 and 1.6 MPa). The inert mass flow rate (at NTP conditions) was adjusted in each test to keep the gas residence time constant within the reactor. The as-received corn stover was pyrolyzed into a biochar without any physical pre-treatment as a way to reduce the operating costs. The properties of biochars showed that high peak temperature led to high fixed-carbon contents, high aromaticity and low molar H:C and O:C ratios; whereas a high pressure only resulted in a further decrease in the O:C ratio and a further increase in the fixed-carbon content. Increasing the operating pressure also resulted in a higher production of pyrolysis gas at the expense of water formation

Image states in metal clusters

The existence of image states in small clusters is shown, using a quantum-mechanical many-body approach. We present image state energies and wave functions for spherical jellium clusters up to 186 atoms, calculated in the GW approximation, where G is the Green's function and W is the dynamically screened Coulomb interaction, which by construction contains the dynamic long-range correlation effects that give rise to image effects. In addition, we find that image states are also subject to quantum confinement. To extrapolate our investigations to clusters in the mesoscopic size range, we propose a semiclassical model potential, which we test against our full GW results

Approximations for many-body Green's functions: insights from the fundamental equations

Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations relating the one-particle Green's function to its functional derivative with respect to an external perturbing potential. In the present work we apply a linear response expansion in order to obtain insights in various approximations for Green's functions calculations. The expansion leads to an effective screening, while keeping the effects of the interaction to all orders. In order to study various aspects of the resulting equations we discretize them, and retain only one point in space, spin, and time for all variables. Within this one-point model we obtain an explicit solution for the Green's function, which allows us to explore the structure of the general family of solutions, and to determine the specific solution that corresponds to the physical one. Moreover we analyze the performances of established approaches like $GW$ over the whole range of interaction strength, and we explore alternative approximations. Finally we link certain approximations for the exact solution to the corresponding manipulations for the differential equation which produce them. This link is crucial in view of a generalization of our findings to the real (multidimensional functional) case where only the differential equation is known.Comment: 17 pages, 7 figure

Image-potential band-gap narrowing at a metal/semiconductor interface

GW approximation is used to systematically revisit the image-potential band-gap narrowing at metal/semiconductor interfaces proposed by Inkson in the 1970's. Here we have questioned how the narrowing as calculated from quasi-particle energy spectra for the jellium/Si interface depends on $r_s$ of the jellium. The gap narrowing is found to only weakly depend on $r_s$ (i.e., narrowing $\simeq 0.3$ eV even for a large $r_s = 6)$. Hence we can turn to smaller polarizability in the semiconductor side as an important factor in looking for larger narrowing.Comment: 6 pages, 7 figure

Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness

The activation gaps for fractional quantum Hall states at filling fractions $\nu=n/(2n+1)$ are computed for heterojunction, square quantum well, as well as parabolic quantum well geometries, using an interaction potential calculated from a self-consistent electronic structure calculation in the local density approximation. The finite thickness is estimated to make $\sim$30% correction to the gap in the heterojunction geometry for typical parameters, which accounts for roughly half of the discrepancy between the experiment and theoretical gaps computed for a pure two dimensional system. Certain model interactions are also considered. It is found that the activation energies behave qualitatively differently depending on whether the interaction is of longer or shorter range than the Coulomb interaction; there are indications that fractional Hall states close to the Fermi sea are destabilized for the latter.Comment: 32 pages, 13 figure