Stefan Albrecht and Lucia Reining
Laboratoire des Solides Irradies, URA 1380 CNRS -- CEA/CEREM, Ecole Polytechnique, F-91128 Palaiseau, France
Rodolfo Del Sole and Giovanni Onida
Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica dell'Universita di Roma Tor Vergata
We discuss details of our approach for the ab initio calculation of excitonic effects in optical properties[1-3]. In particular, we test the validity of various approximations in the ingredients of the calculation.
[1] G. Onida, L. Reining, R.W. Godby, R. Del Sole, and W. Andreoni, Phys. Rev. Lett. 75, 818 (1995); [2] S. Albrecht, G. Onida, and L. Reining, Phys. Rev. B 55, 10 278 (1997); [3] S. Albrecht, L. Reining, R. Del~Sole, and G. Onida, Phys. Rev. Lett. 80, 4510 (1998).
Mauro Boero, Exeter University, U.K.
Double-barrier resonant dot structures are ideal to study the transport properties of quantum dots and to obtain important information on the spectrum and wave functions of zero-dimensional structures. In this work we present a theoretical study which enables to calculate the I_V characteristics of both 1D-0D-1D and 3D-0D-3D structures. The calculations are comapred with the experimenatl findings and good agreement is obtained. This work renders the interpretaion of experimental results clearer and allows to directly access details of the confined wave functions such as spatial extension and angular momentum.
John F. Dobson, Griffith University, Australia
Both hydrodynamics and the well-known adiabatic LDA can be regarded as time-dependent local density approximations. In the case of hydrodynamics, the independent-particle kinetic energy or the pressure term is approximated locally, whereas in the adiabatic LDA these effects are treated microscopically and it is the exchange-correlation effects which are treated locally. When dealing with such local-density approximations for high-frequency phenomena, one must recognize that these quantities cannot be taken from the static properties of the corresponding homogeneous system, but have an intrinsic frequency dependence in the linear case. Equivalently, in the time domain, a memory is present in pressure or xc kernels, and this formulation applies to the nonlinear case as well. A simple modification of the usual local-density approximation will be discussed. It allows simple results to be derived while taking care of various constraints along with the description of memory effects.
GW calculations and photoemission experiments in solids. On the example of a few II-VI semiconductors, I will discuss an impact of the dynamics of excited electrons and the final-states dispersion on the experimental determination of the band structure of solids. I will argue, that a dynamical GW calculation can substantially improve the mapping of band structures from the experimental, photoemission, energy-distribution curves.
F.Flores, P.Pou, J.Ortega, R.Pirez, A.Levy-Yeyati and A.Martin-Rodero, Departamento de Fisica Teorica de la Materia Condensada de Madrid, Spain
We present a self-consistent LCAO-OO approach for calculating the electronic properties of solids and their quasi-particle spectra.In In this approach a LCAO-hamiltonian is introduced using a local orbital basis and quantum-chemistry techniques.Then, many-body effects are analyzed by calculating the exchange-correlation energy as a function of the diffe- rent orbital occupancies(OO). Selfconsintency yields the cohesive energy of the solid and a one-electron density of states equivalent to the one calculated in LD.In a final step, a local self-energy is introduced to calculate the quasi-particle spectrum. This self-energy is an interpo- lation between a low and a highly correlated limit. We shall discuss the equivalence with the GW-approach.An example for NiO will be presented.
J. Furthm\"uller and F. Bechstedt, Institut f\"ur Festk\"orpertheorie und Theoretische Optik, Friedrich-Schiller-Universit\"at Jena, Max-Wien-Platz 1, D-07743 Jena
The simplest approaches which allow the calculation of reasonable excitation energies are the $\Delta$SCF approach, Slater's transition state theorem or the self-interaction correction (SIC) scheme. This is demonstrated for free atoms. However, these approaches are problematic or fail for extended systems, e.g., the answer depends on the representation of the wave functions (extended Bloch states vs. localized Wannier orbitals). An interesting approximation avoiding problems in the case of extended systems is provided by the atomic projector formalism proposed by Pollmann et. al (so-called ``self-interaction-corrected pseudopotentials''). However, in its current version Pollmann's scheme raises new problems. One key problem is related to the shape of the atomic projectors. Another one is related to the ``configuration dependence'' of the corrections. Therefore, we propose a modified version of this scheme within the framework of Vanderbilt's ultrasoft pseudopotentials which might help to avoid or to reduce some of the problems.
O.V. Gritsenko (*,**), S.J.A. van Gisbergen (**), F.Kootstra (***), P.R.T. Schipper (**), J.G. Snijders (***), E.J. Baerends (**)
(*)Departamento de Fisica Teorica, Universidad de Valladolid, E-47011 Valladolid, Spain
(**)Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
(***)Department of Chemical Physics and Materials Science Centre, Rijksuniversiteit Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
The benchmark calculations of the polarizabilities and excitation energies of the He and Be atoms and the polarizabilities of the Ne atom and the molecules H2, N2, HF, HCl, H2O, CO are performed within the linear-response time-dependent density functional theory (TDDFT) with the accurate exchange-correlation (xc) potentials constructed from ab initio electron densities and with various approximate xc kernels. They are compared with calculations performed with xc potential of the local density approximation (LDA) as well as with the van Leeuwen-Baerends (LB94) xc potential. The results depend essentially on the quality of the xc potentials used in the calculations. The combination of the accurate xc potential with the xc kernel of the adiabatic local density approximation (ALDA) provides a good quality of the calculated dipole and quadrupole polarizabilities. The differences of the energies of the Kohn-Sham orbitals obtained with the accurate xc potentials yield a reliable estimate of the corresponding excitation energies for He and Be, with the exception of the lowest excitation energies. The addition of the ALDA xc kernel provides, in general, further improvement of the results with the exception of the singlet 1s-2p excitation in He, the singlet s-d and the triplet 2s-4p excitations in Be.
E.K.U. Gross, University of W"urzburg, Germany
We describe the calculation of excitation energies from time-dependent density functional theory and present recent results for molecular systems. Furthermore, time-dependent density functional theory and the adiabatic connection formula are used to derive new approximations for the total correlation energy functional which correctly reproduce the the van der Waals 1/R^6 behavior in the limit of two separated neutral subsystems. From these functionals we calculate both total correlation energies and van der Waals coefficients, thus demonstrating the feasibility of a "seamless" functional.
M. Fleck, A. I. Liechtenstein, A. M. Oles, and L. Hedin
Using the dynamical mean field theory we analyzed commensurate and incommensurate magnetic order within the two-dimensional Hubbard model. Electron correlations stabilize spin spiral order in the doped systems. We show that short-range anti-ferromagnetic correlations induce new structures in the one-particle excitation spectra. The properties of the pseudo-gap are discussed in connection with the optical properties of the system. Using realistic parameters for the cuprates some of the anomalies of the Mott-Hubbard systems can be understood.
L. Hedin, John Michiels, John Inglesfield, Witold Bardyszewski, John Rehr
Valerio Olevano, Maurizia Palummo, Giovanni Onida, Rodolfo Del Sole, Dipartimento di Fisica, Universita' di Roma Tor Vergata, Rome , Italy.
The macroscopic dielectric function of crystalline silicon is evaluated taking into account non-local parts of the exchange and correlation. The electronic structure (one-electron energies and wavefunctions) is calculated within the density-functional theory using an energy functional beyond the local density approximation. Non-local density contributions in the functional are considered using an expression based on the exchange-correlation kernel of the homogeneous electron gas. This q-dependent exchange-correlation kernel is also kept into account in the evaluation of the test-charge dielectric matrix. Local-fields are taken into account in the standard Adler-Wiser approach. Results on the macroscopic dielectric function evaluated in the limit of vanishing q are reported compared with the RPA and LDA values. The value of the NLDA dielectric constant improves with respect to the LDA.
1. Summary of the advantages and drawbacks of Configuration Interaction (CI) methods in the calculation of excited state properties
2. Benefits and drawbacks of the Cluster approach
3. Examples, and applications to Oxide materials
Michael Rohlfing, University of California,366 LeConte Hall # 7300, Berkeley, CA 94720-7300, USA
We present an ab-initio approach to calculate the optical absorption spectrum of non-metallic materials. This is done by solving the Bethe-Salpeter equation for the two-particle Green's function of electron-hole pairs, fully including the electron-hole interaction kernel. The calculations are based on ab-initio quasiparticle band-structure calculations within the GW approximation. This is a general method that allows us to study bound excitonic states and the continuum absorption spectrum of a wide range of materials. We will discuss results for periodic bulk crystals, for isolated Si clusters, as well as, for one-dimensional conducting polymers.
Arno Schindlmayr and Thomas J. Pollehn Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, UK
R. W. Godby Department of Physics, University of York, Heslington, York YO10 5DD, UK
With the aim of identifying universal trends, we compare fully self-consistent electronic spectra and total energies obtained from the GW approximation with those from an extended GWGamma scheme that includes a nontrivial vertex function and the fundamentally distinct Bethe-Goldstone approach based on the T-matrix. The self-consistent Green's function G, as derived from Dyson's equation, is used not only in the self-energy but also to construct the screened interaction W for a model system. For all approximations we observe a similar deterioration of the spectrum, which is not removed by vertex corrections. In particular, satellite peaks are systematically broadened and move closer to the chemical potential. The corresponding total energies are universally raised, independent of the system parameters. Our results therefore suggest that any improvement in total energy due to self-consistency, such as for the electron gas in the GW approximation, may be fortuitous.
E. L. Shirley, L. X. Benedict, R. B. Bohn
NIST, Gaithersburg, Maryland 20899 U.S.A.
We present a computationally efficient scheme to treat optical absorption and the valence exciton problem in real materials. The approach used [1] relies on iterative techniques to solve the two-particle (electron plus hole) Schroedinger equation. These can include computing absorption spectra using the Lanczos or Haydock Recursion Method, or iterative inversion of the Hamiltonian, H. Action of H on a wave function, which is the most demanding part of the calculations, is carried out efficiently by acting with each term in H in a representation in which the term is diagonal. Aspects of the scaling will be discussed. Results will be presented for LiF, MgO, CaF_2, Si, diamond, Ge, GaAs, wGaN, zGaN, including comparison with experiment.
[1] L. X. Benedict, E. L. Shirley, and R. B. Bohn, Phys. Rev. Lett. 80, 4514 (1998), Phys. Rev. B 57, R9385 (1998).
L. Steinbeck, I.D. White*, A. Rubio+, R.W. Godby and L. Reining^
Department of Physics, University of York, Heslington, York YO10 5DD, UK
*Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
+Departamento Fisica Teorica, Universidad de Valladolid, E-47011 Valladolid, Spain
^Laboratoire des Solides Irradies, Ecole Polytechnique, 91128 Palaiseau, France
The real-space imaginary-time GW method [1] for the calculation of self-energies and quasiparticle excitation energies for solids has been developed further to allow larger systems to be studied than previously possible. The application of the method to self-energy calculations for III-V semiconductors is discussed and first results are reported.
[1] H. N. Rojas, R. W. Godby, and R. J. Needs, Phys. Rev. Lett. 74, 1827 (1995); M. M. Rieger, L. Steinbeck, I. D. White, H. N. Rojas, and R. W. Godby, submitted for publication
M. Torrent (*,+) and L. Reining (*)
(*) Laboratoire des Solides Irradies. Ecole Polytechnique. 91128 Palaiseau. FRANCE
(+) CEA-Bruyeres le Chatel. 91680 Bruyeres le Chatel. FRANCE
We discuss the difficulties of performing electronic structure calculations of clusters in a plane-wave basis. With the help of a simple model, we study possible ways to improve convergence of the results with the supercell size.
Robert van Leeuwen
Institut fuer Theoretische Physik, Universitaet Wuerzburg, Wuerzburg, Germany
For the development of new time-dependent exchange-correlation functionals in time-dependent density functional theory (TDDFT) it is useful to make some connections between TDDFT and the many-body Green function approach. In TDDFT the energy-functional must be replaced by an action functional. All response functions are then obtained as higher functional derivatives of this action functional. As the familiar relation in TDDFT between densities and potentials involves retarded, rather than time-ordered quantities, use will be made of the Keldysh Green function method, which incorporates both types of response functions in a natural way. I will focus on a TDDFT-approach to the calculation of the polarization propagator and the one-particle Green function.
Return to the workshop's programme (or use your browser's Back button)