Abstract
This paper shows how to calculate the full mixed dynamic structure factor including excitonic effects from first principles. The calculations shows good agreement between their calculations and X-ray Scattering experimental results for bulk silicon and Lithium Fluoride. The authors extend the full mixed dynamic structure factor theory to determine the exchange-correlation kernel of Time-Dependent Density Functional Theory in its full matrix form.
Highlights
One of the key concepts in condensed matter theory is screening, the modification of a potential felt by a charge due to the rearrangement of other charges [1]
The densitydensity response function is measured directly or indirectly in many spectroscopy experiments [3], such as electron energy loss spectroscopy (EELS) [4], optical absorption [5,6], or inelastic x-ray scattering (IXS) [7], which yields the dynamic structure factor (DSF) that is proportional to the imaginary part of χ
Some important features of the frequency-dependent screening are captured for the homogeneous electron gas by the Lindhard dielectric function [11] from the random phase approximation (RPA) [12], where only the classical electrostatic potential between charges is taken into account
Summary
Igor Reshetnyak ,1,2,* Matteo Gatti, Francesco Sottile ,1,2 and Lucia Reining1,2 1Laboratoire des Solides Irradiés, École Polytechnique, CNRS, CEA/DRF/IRAMIS, Institut Polytechnique de Paris, F-91128 Palaiseau, France 2European Theoretical Spectroscopy Facility (ETSF). The RPA cannot yield bound excitons [25], which are most clearly seen in optical spectra [26,27] Such many-body effects are instead captured by the Bethe-Salpeter equation (BSE) [28], a twobody Dyson equation that correlates the excited electrons and holes [25,29]. In an inhomogeneous material even a spatially monochromatic perturbation creates a response on different length scales [56,57], depending on the local structure of the material When all these components of the response are known can one describe induced charges with spatial resolution, and can one determine important many-body effects that depend on all the components of W.
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