Rodolfo Del Sole

Ab Initio Calculation of Excitonic Effects in the Optical Spectra of Semiconductors

An ab initio approach to the calculation of excitonic effects in the optical absorption spectra of semiconductors and insulators is formulated. It starts from a quasiparticle band structure calculation and is based on the relevant Bethe-Salpeter equation. An application to bulk silicon shows a substantial improvement with respect to previous calculations in the description of the experimental spectrum, for both peak positions and line shape.

Time-dependent density-functional theory for extended systems

For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schrequation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schr¨ odinger equations—the Kohn-Sham equations. The complication of the problem is hidden in the— unknown—time-dependent exchange and correlation potential that appears in the Kohn-Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe- Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems. (Some figures in this article are in colour only in the electronic version)

Quasiparticle electronic structure of copper in the GW approximation

We show that the results of photoemission and inverse photoemission experiments on bulk copper can be quantitatively described within band-structure theory, with no evidence of effects beyond the single-quasiparticle approximation. The well-known discrepancies between the experimental band structure and the Kohn-Sham eigenvalues of density functional theory are almost completely corrected by self-energy effects. Exchange-correlation contributions to the self-energy arising from 3s and 3p core levels are shown to be crucial.

Many-body perturbation theory using the density-functional concept: beyond the GW approximation

We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.

First-principles calculation of the plasmon resonance and of the reflectance spectrum of silver in the GW approximation

We show that the position and width of the plasmon resonance in silver are correctly predicted by ab initio calculations including self-energy effects within the GW approximation. Unlike in simple metals and semiconductors, quasiparticle corrections play a key role and are essential to obtain electron energy loss in quantitative agreement with the experimental data. The sharp reflectance minimum at 3.92 eV, that cannot be reproduced within density-functional theory ~DFT! in the local-density approximation ~LDA!, is also well described within GW. The present results solve two unsettled drawbacks of linear-response calculations for silver.

Reflectance anisotropy spectra of Cu and Ag (110) surfaces from ab initio theory

Reflectance anisotropy spectra of Cu and Ag (110) surfaces are obtained by ab initio calculations. We disentangle the effects of the intraband and interband parts of the bulk dielectric function in ...

FIRST–PRINCIPLES OPTICAL SPECTRA OF SEMICONDUCTOR SURFACES: FROM ONE-PARTICLE TO MANY-BODY APPROACH

The experimental characterization of surfaces is often obtained through spectro scopic techniques like photoemission inverse photoemission electron energy loss spectroscopy and optical techniques as Reflectance Anisotropy and Differential Reflectivity etc It is hence very important to describe accurately the electronic excitations with highly reliable and efficient ab-initio approaches In the last two decades Density Functional Theory has proven to be a very powerful tool for elec tronic ground state properties but shows significant deviations from the expen ments when excited states are involved The use of many body Green’s functions theory, with DFT calculations as zero order approximation is now the state of the art to obtam quasi particle excitation energies and optical spectra both in bulk and at surfaces In this paper we will present the current status of this theoretical and computational approach showing results for several semiconductor surfaces

Susceptibility model for the homogeneous electron gas

We calculate the exchange-correlation energy of the homogeneous electron gas using the adiabatic connection formula and a simple model for the susceptibility. The exact exchange energy is recovered and a formula is obtained for the correlation energy, which is in good agreement with previous results. This approach is meant to be a starting point for obtaining a charge-conserving energy functional suitable for describing inhomogeneous systems.

Ab initio calculation of excitonic effects in realistic materials

Ab initio calculations, based on the density functional theory (DFT) in the local density approximation (LDA), allow for the description of the ground state properties of a wide class of materials. Also one-quasiparticle excitations can be obtained with good precision by adding self-energy corrections to the DFT-LDA eigenvalues. A realistic description of two-particle excitations, like the creation of electron-hole pairs in absorption experiments, is hardly feasible for systems where the electron and the hole interact. In this work we show how such excitonic effects can be included in ab initio electronic structure calculations, via the solution of an effective two-particle equation. Results for different systems are presented.

On the Theory of Second Harmonic Generation

In Sect. 1.5, second-harmonic and sum-frequency generation (SHG and SFG) at surfaces and interfaces was introduced. Experimental results are discussed in Chapter 8. Various aspects of the theory of SHG at surfaces and interfaces are discussed in this chapter.