We present a first-principles calculation of the conductivity tensors
relevant to study the linear and second-harmonic optical response from
thin films. The calculations are done within the framework of the electric-dipole
approximation and includes the Lindhard screening term. The formalism is
presented. Numerical results are obtained using the WIEN95/97 FLAPW code
with our own implementation of spin-orbit coupling and the optical response.
The films we consider consist of a monolayer of Fe and 1--7 monolayers
of Cu. We show that the band structure and the density of states converge
when we add more Cu layers to the structure. The nonlinear optical response,
however, is much more difficult to converge than the electronic structure.
Si and Ge nanocrystals embedded in a wide-gap semiconductor like $\alpha$-SiC are potentially interesting systems for possible electroluminescence applications. A theoretical understanding of these systems is yet to be achieved, both for the optical properties under inclusion of the relevant many-body effects and for the structural and electronic properties. We present first attempts to describe these properties using parameter-free electronic structure calculations and large supercells. A plane-wave-pseudopotential code (VASP ) is used to calculate the electronic structure within density-functional theory (DFT) in local-density approximation (LDA). Ultrasoft non-normconserving pseudopotentials allow the {\it ab-initio} treatment of supercells with up to 512 atoms, even in the case of first-row elements. Each supercell contains one cluster, the remaining space is filled with matrix material. The maximum dot diameters are about 1 nm. Examples are mainly structures made of group-IV materials. In the present talk we focus our attention on three main problems.
[1] P.E. Bl{\"o}chl, Phys. Rev. B{\bf 50}, 17953 (1994)
[2] C.J. Pickard and M.C. Paine, Phys. Rev. B{\bf 59}, 4685 (1999)
[3] F. Bechstedt, R. Del Sole, G. Cappellini, and L. Reining, Solid
State Commun. {\bf 84}, 765 (1992); G. Cappellini, R. Del Sole, L. Reining,
and F. Bechstedt, Phys. Rev. B{\bf 47}, 9892 (1993)
The ``linear combination of bulk bands'' (LCBB) method [1] permits to calculate the single-particle electronic states of nanostructure systems, within an empirical pseudopotential framework. This method is particularly suitable for large scale superlattices, wires and dots, since it consists of writing the wave functions of the quantum states as linear combinations of Bloch eigenstates of the constituent bulk materials, over band indices $n$ and wave vectors ${\bf k}$. The potential term in the Hamiltonian is built as a superposition of screened, spherical atomic pseudopotentials $v_{\alpha} ({\bf r})$, that are extracted from local density approximation calculations (LDA) on bulk systems and then adjusted empirically [2]. Unlike tight-binding or plane wave expansions, the LCBB expansion allows the intuitive pre-selection of physically important states to be included in the basis set, resulting in an easily manageable Hamiltonian matrix. Unlike ${\bf k} \cdot {\bf p}$ approach, off-$\Gamma$ states $u_{n,{\bf k} \neq 0}$ are directly considered, eliminating the need for many ${\bf k} = 0$ bulk states to describe $k \gg 0$ states. Moreover, the geometrical details of the structure are not lost and couplings are fully included. In this work we present the application of LCBB method to (001) superlattices (SL's). The band structure across all the tetragonal first Brillouin zone (BZ) is calculated for both (GaAs)$_m$/(Alas)$_m$ and (GaAs)$_m$/(vacuum)$_m$ SL's, for different values of $m$, and compared to bulk band structure folded in the tetragonal BZ. In (GaAs)$_m$/(vacuum)$_m$ SL's dangling bonds give rise to surface states which lie in the forbidden energy gap. The optical properties of these systems can be described, in first approximation, in terms of one-electron transitions produced by a perturbative electromagnetic Hamiltonian. The LCBB empirical pseudopotential approach allows calculations of optical spectra of heterostructures with a reasonably small computational time. Confinement and folding effects are well described [3]; on the other hand it isn't possible to neglect local field effects to account for optical anisotropies [4]
[1] L.W.Wang, A.Franceschetti and A.Zunger, {\sl Phys. Rev. Lett.} {\bf 78} 2819 (1997).
[2] [2.] K.A.M\"ader and A.Zunger, {\sl Phys. Rev. B} {\bf 50}, 17393 (1994).
[3] M.Garriga, M.Cardona, N.E.Christensen, P.Lautenschlager, T.Isu and K.Ploog {\sl Phys. Rev. B} {\bf 36}, 3254 (1987)
[4] A.A.Sirenko, P.Etchegoin, A.Fainstein, K.Eberl and M.Cardona {\sl
Phys. Rev. B} {\bf 60}, 8253 (1999).
One of the most challenging problems concerning semiconductor nanocrystals remains the accurate prediction of their excitonic energy gap. For silicon, a number of calculations of the independent particle gap have been performed based either on empirical techniques (tight binding [1] or pseudopotentials [2]) or on the ab initio local density approximation (LDA) [3]. In the latter case, as LDA underestimates the bulk bandgap, the results are usually shifted by the bulk correction. Interestingly these corrected LDA bandgaps are in quite good agreement with the best tight binding or pseudopotential results [3,4]. The second step has usually been to substract from this value the screened direct electron-hole attraction. However the whole procedure is not clearly justified and conflicting points of view [5-7] have been expressed concerning its validity. The aim of this work is thus to clarify this problem. We present calculations of the one and two particle excitations in silicon nanocrystals. The one-particle properties are handled in the GW approximation and the excitonic gap is obtained from the Bethe-Salpeter equation. We develop a tight binding version of these methods to treat clusters up to 275 atoms. The self-energy and Coulomb corrections almost exactly cancel each other for crystallites with radius larger than 0.6 nm. The result of this cancellation is that one-particle calculations give quite accurate values for the excitonic gap of crystallites in the most studied range of sizes. We also show that the self-energy and Coulomb corrections are dominated to a large extent by classical electrostatic contributions.
[1] J.P. Proot, C. Delerue and G. Allan, Appl.Phys.Lett. 61, 1948 (1992); C. Delerue, G. Allan and M. Lannoo, Phys.Rev.B 48, 11024 (1993)
[2] Lin-Wang Wang and A. Zunger, J.Phys.Chem. 98, 2158 (1994).
[3] B. Delley and E.F. Steigmeier, Phys.Rev.B 47, 1397 (1993); Appl.Phys.Lett. 67, 2370 (1995).
[4] M. Lannoo, G. Allan and C. Delerue, in "Structural and Optical Properties of Porous Silicon Nanostructures", G. Amato, C. Delerue, H.-J. von Bardeleben Eds (Gordon and Breach Science Publishers, Amsterdam, 1997) p. 187.
[5] S. ^Zg^Zt, J. R. Chelikowsky, and S. G. Louie, Phys. Rev. Lett. 79, 1770 (1997).
[6] R.W. Godby and I.D. White, Phys.Rev.Lett. 80, 3161 (1998).
[7] A. Franceschetti, L.W. Wang, and A. Zunger, Phys. Rev. Lett. 83,
1269 (1999).
The interacting density-density response function of an inhomogeneous
electronic system has poles at frequencies equal to exact excitation energies.
In time dependent density functional theory (TDDFT), all aspects of the
response beyond the RPA are described by the exchange-correlation kernel
$f_{xc}$, or equivalently the dynamic local field factor $G$. This quantity
is in general spatially and temporally nonlocal, but early TDDFT calculations
assumed $f_{xc}$ to be local in both domains. Numerical experimentation
suggests that the temporal locality assumption is surprisingly good in
many systems, so that it is worthwhile to consider spatial nonlocality
alone. The Singwi-Tosi-Land-Sjolander (STLS) approach represents an attempt
to find an optimal spatially nonlocal field factor, based on a heuristic
factorization of the dynamic pair distribution. It has the unique feature
that the static pair distribution is selfconsistently determined in the
process. This approach is rather successful for correlation energies and
plasmon properties of weakly to moderately correlated uniform electron
gases. It apparently has not so far been applied to nonuniform gases, presumably
because of the increased computational complexity. Recent work on the full
RPA description of inhomogeneous systems suggests that the STLS scheme
is now well within computational reach, at least for geometrically simple
inhomogeneous systems such as jellium surfaces and atoms. The STLS theory
does require some modification for inhomogeneous systems, and some aspects
of this problem will be discussed.
In GW calculations of the quasiparticle spectra of real systems consisting of many atoms per unit cell, such as surfaces, alloys, and disordered solids, the main bottleneck is represented by the computation of the response functions from first principles. In this work, we discuss an effective approach devised to limit the computational workload, which is nevertheless applicable to a large class of materials, ranging from elemental semiconductors to transition metal oxides.
Firstly, we find the ground-state electron density, in the framework of the density functional theory (DFT), with and without a weak test potential, placed in various sites of the crystal. We have thus access to the "exact" induced density in direct space, which depends on the center of mass of the test potential in a parametric way. Then, we compute an approximate static polarizability, built from N inoccupied bands and a residual term in which the missing empty states are replaced with plane waves [1] weighted by a coefficient depending on the local electron density. This allows us to choose N as small as possible for a given desired accuracy in the resulting induced density. Applications to bulk Si, MgO and strontium titanate are presented.
Moreover, we discuss the reliability of model dielectric functions in which the local field effects are taken into account through a parametric dependency on the electron density, such as that proposed by Bechstedt and Del Sole [2]. The peculiarities of an alternative approach will be stressed, especially for systems with localized electron states around the fundamental gap, such as strontium titanate, where the Bechstedt-Del Sole approach fails to provide the correct fundamental band gap [3].
[1] L.Steinbeck et al, Comp.Phys.Comm. 125, 105 (2000)
[2] F. Bechstedt and R. Del Sole, Phys. Rev. B 38, 7710 (1988)
[3] G. Cappellini et al, J.Phys.Cond.Matt.12, 3671 (2000)
In the framework of Many-Body Perturbation Theory (MBPT), the total energy of a system of interacting electrons can be calculated via the Galitskii-Migdal formula. This requires an accurate knowledge of the one-particle Green's function of the system in a very long range of frequencies. The Green's function can be calculated within the self-consistent $GW$ approximation, which has led to accurate total energies when applied to homogeneous electron gases [1,2]. However this approach is computationally very expensive and at the moment its application to complex systems of industrial interest is not feasible.
We propose a model, based on self-consistent $GW$ results for the homogeneous electron gas, which contains an accurate description of the non-locality and frequency-dependence of the self-energy. This model allows one to calculate total energies without significantly increasing the numerical cost of standard density-functional theory calculations, thus making it useful for applications to large systems. The method has been tested against accurate quantum Monte Carlo results for the linear response of the homogeneous electron gas and structural properties of bulk silicon.
[1] B. Holm and U. von Barth, Phys. Rev. B {\bf 57}, 2108 (1998).
[2] P. Garc\'{\i}a-Gonz\'alez and R. W. Godby (unpublished).
For the last thirty years, Density Functional Theory (DFT) has been the standard for obtaining the ground-state properties of many-electron systems. However, the increasing computational speed and capacity allow the study of a growing number of complex systems using DFT. Although in many cases amazing new results have been obtained (specially when complemented with molecular-dynamics), there are more and more situations where the limitations of the standard approximations in DFT are evident. On the other hand there is a number of exact formal properties that such common implementations of the DFT fail to fulfil. The main problem is that, being DFT an exact theory, it relays on the description of many-body effects (that are highly non-local) by means of a local potential. Generalizations of the DFT allowing the use of non-local potentials have been recently proposed, but some fundamental tests (like the description of the linear response in the homogeneous limit) seem to be too sensitive to the details of the functionals so developed.
Green's function many body perturbation theories (like Hedin's GW approximation) can provide a different way to overcome the limitations of present DFT. In the GW the non-local effects are taken directly into account, and the Coulomb interaction is dynamically screened. Both things are done in a closed way, without the resort of additional models albeit those inherent to the GW theory itself. Moreover, the interacting Green's function G is the final output of any GW calculation and the knowledge of G is enough to determine many ground-state properties, including the electron density and the total energy.
The above comments suggest that GW approximation might be a very valuable way for determining ground-state properties, but such hypothesis has to be confirmed with actual implementations of the theory. So far, the performance of GW in these types of calculations has been only tested in some model system and in the homogeneous electron gas (HEG) in the range of metallic densities. In this work we present GW results for the ground-state of HEG, covering a broad range of densities in both spin-unpolarized and fully spin-polarized phases.[1] Other issues, such as conservation of the number of particles and possible implications in the development of simpler models to calculate total energies will be also discussed.
[1] P. Garcia-Gonzalez and R. W. Godby, Bull. Am. Phys. Soc. 45, 72
(2000) and to be published
We calculate the charge density of mono-, di- and trivalent Cu compounds, and demonstrate that the difference in the net Cu charge is very much smaller than the formal valence would suggest.
The chemical shift nevertheless behaves in the expected way, with the strongest core-level binding energy for the trivalent compound.
We then focus on the shape of the core-level spectrum, and show that there is a large difference between the mono- and divalent compounds and a less pronounced difference between di- and trivalent compounds. For the divalent compounds the dependence of the spectrum on the Cu-O network is studied extensively. Although the core spectrum is usually considered as a local probe, the line shape depends rather sensitively on the coupling Cu-O-Cu to the second nearest neighbor (Cu) sites. We show that this behavior can be rather well reproduced in the Anderson impurity model. The reason for the dependence on the Cu-O network is analyzed.
Owing to the rapid developments in laser technology, ultra-short high-intensity laser pulses have become available in recent years. Considering the interaction of such extreme radiation fields with matter, one observes a wealth of exciting new phenomena which cannot be explained by ordinary perturbation theory.
A consistent ab-initio approach to the strong-field dynamics of atomic or molecular systems should thus allow for a non-perturbative treatment of the external radiation field as well as for an appropriate description of the quantum behavior of the electronic and nuclear degrees of freedom involved. For that purpose, we propose a {\it time-dependent multicomponent density-functional} approach to molecules in intense laser pulses. It is shown that this method provides a numerically efficient way to calculate the strongly non-linear dynamics of an interacting many-particle system.
After an overview over the fundamental theorems, we investigate approximations for the time-dependent effective potentials which, in particular, contain the exchange-correlation effects of the system. The method is then used to discuss the strong-field behavior of a simple model system.
Comparisons to exact solutions allow us to assess the quality of the
approximations employed within the proposed multicomponent density-functional
scheme.
Quantum measurement theory based on the von Neumann projection postulate [1] fails if the measured quantity relates to a finite duration rather than one instant of time. In this case a quantum system must be observed for a finite time and the measurement amplitude cannot, in general, be obtained by projecting its Schroedinger state on an eigenfunction of a hermitian operator. By defining a quantum measurement as destruction of coherence between certain components of Schroedinger wavefunction,we introduce a new approach which generalize von Neumann theory to finite time and continuous measurements. As examples of application of the new method, we analyze the quantum measurements of the traversal time [2] and the time average of a dynamical variable.
[1] J.von Neumann, Mathematical Foundation of Quantum Mechanics, (Princeton University Press, NJ, 1955)
[2] D. Sokolovski, Phys. Rev. Lett., 79, 4946(1997)
NiO is a paradigm magnetic oxide whose properties have been studied extensively for many years. There now exist good optical, EELS and other data on the low energy excitations in the range ~ 1 - 5 eV for stoichiometric NiO, and, importantly, also for LixNi1-xO, on the basis of which theory and computation can be assessed. In this talk I will first summarise this data and draw certain conclusions which have suggested(forced?)a direct approach to the calculation of the local d-d excited states both for the bulk and (100) surface [1,2]. I will then consider the strong optical absorption at ~ 4 eV in relation to the band gap, (I+A) and charge-transfer excitations, based on both HF and KS approaches and consider, briefly, the contribution of electron correlation to these quantities.
[1] C.Noguera and W.C.Mackrodt, J.Phys.:Condensed Matter 12, 2163 (2000)
[2] W.C.Mackrodt and C.Noguera, Surface Science - In press
Using a recently developed scheme for performing, within density functional
theory, molecular dynamics and geometry optimisation for fairly large systems
in the first excited singlet state, we have studied the structure and energy
changes that the rhodopsin chromophore undergoes during the photoisomerisation
from 11-cis to all-trans. We discuss the effects of relevant parts of the
protein environment close to the chromophore on the isomerisation barrier
and on the chromophore structure.
[C. Molteni et al., J. Am. Chem. Soc. 121, 12177 (1999)]
Dipartimento di Chimica, Universita'di Firenze
Laura Moroni, Cristina Gellini, Pier Remigio Salvi and Vincenzo Schettino
Dipartimento di Chimica, Universita' di Firenze
Via G. Capponi 9, 50121 Firenze (ITALY)
Electronic properties of retinal cromophores, and in particular of all-trans retinal, have been studied since long time in relation to the cis-trans photoisomerization of photoactive proteins(1). Much less is known about excited state dynamics in the crystal phase.
The fluorescence spectra of polycrystalline all-trans retinal (ATR) have been measured at 77 K as a function af exciting wavelength between 420 and 500 nm, i.e., below the energy of the lowest excited state of all trans retinal. By comparison with solution spectra at high concentration, emission from dimers and more associated species have been identified. On the same time, ab-initio calculations with the B3-LYP exchange-correlation functional and using the 6-31G* basis set have been performed on (ATR)n (n=2,3,4) species.
These calculations show that isolated clusters of all-trans retinal are stable in the ground state and suggest that these aggregates may be responsable of the observed fluorescence. It is hoped that theoretical ab-initio models may be developed to give a correct estimate of excited levels of clusters.
Reference
1. R. R. Birge, Biophys. Acta 1016 (1990) 293-327
Although many body perturbation theory (MBPT) for quite some time has been used to determine quasiparticle energies and optical properties of solids, traditionally the issue of ground state energy has not been addressed with this method. Rather, most efforts in that direction have been concentrating on various mean field theories. The success of density functional theory (DFT) has enhanced this evolution. However, there are certain systems for which known approximations for the so called exchange-correlation potential within DFT cannot correctly reproduce the observed ground states or the calculated groundstate properties deviate significantly from experiment. In situations like these, an alternative is to have a theory that does not depend on such approximations, but rather is derived from first principles within MBPT, albeit with some other form of approximation. We here investigate two such schemes, rather closely related to each other, in order to highlight the essential properties of a MBPT that correctly describes spectral properties {\it and} ground state energies. As a first step, we have investigated the case of the electron gas which provides a starting point for more general cases of real materials.
We present a fully ab initio GW calculation for diamond. Our approach
differs from conventional GW techniques for semiconductors, which start
out with a pseudo- potential plus LDA calculation in a plane-wave basis.
Our starting point is an all-electron restricted Hartree- Fock calculation
in a Gaussian basis, more appropriate for wide-gap insulators. However,
unlike quantum chemists, we deliberately avoid using contracted Gaussian
shells. This eliminates the need for optimisation of the basis and generates
a large space of virtual states. The centre-piece of the GW technique is
calculation of the inverse dielectric function. A common approach here
is to use the plasmon-pole approximation based upon the concept of dielectric
band structure, where the dielectric function is expanded over a basis
of eigenpotentials. We present calculations of the most important eigenpotentials
and demonstrate the multipolar nature of screening modes located on atomic
and/or bond sites. The fundamental gap, grossly exaggerated in HFA, is
reduced to values close to the experimental value.
We discuss the emergence of uncommon structures in the case of magnetic iron clusters (Fe_N with N < 25 atoms), where the optimum geometry results from a competition between the exchange interaction favouring open structures and the covalent bonding that favors compact structures.
The lowest energy structures are found to be overall magnetic for the
size range studied. However, particularly stable non-magnetic structures
occur
for N=8,12,14 and 16, which can be interpreted as a spatial replication
of a basic template obtained at N=4. These LEGO-like structures tend to
disappear as the size of the Iron clusters increase, leaving room for the
covalent-exchange interplay mentioned before. This interplay, in turn,
reveals clusters which exhibit an enhanced local stability, and which can
be considered as magnetic magic structures.
Y.Pavlyukh, W.Huebner
Electron relaxation in metal nanoparticles under the influence of a strong femtosecond laser pulse is the object of our theoretical investigation. Our model system is the Pt$_{3}^{-}$ cluster. It has a small number of atoms, which makes its excited-level structure study accessible to ab initio calculations. Due to its dense-level structure [1] the electron-electron relaxation mechanism in that cluster is as important as in bulk metals. This fact makes Pt$_{3}^{-}$ a convenient object of the theoretical investigation of electron dynamics under the influence of femtosecond laser pulses. In this time regime both electron relaxation mechanisms are important: electron-electron and electron-phonon coupling. In our work we compared efficience of these mechanisms by the numerical solution of the two-temperature model equations. However we intend to go beyond the phenomenological level of the theory by using a microscoping approach. FWM experiments on GaAs semiconductors [2] showed the possibility of the coherent control of the electron-phonon quantum kinetics. Application of this idea to our system consists of the following steps:
1. Evaluation of the excited states energies and transition matrix elements within the GWA BSE (Bethe-Salpeter equation).
2. Analysis of the phonon modes by means of group theory.
3. Investigation of the quantum kinetics within the Floquet theory.
At the present time we proceed with the solution of the first problem.
References:
1. N. Pontius, P. S. Bechthold, M.Neeb, and W.Eberhardt, Ultrafast hot-electron dynamics observed in Pt$_{3}^{-}$ using time-resolved photoelectron spectroscopy, Phys. Rev. Lett. 84, 1132 (2000).
2. M. U. Wehner, M. H. Ulm, D. S. Chemla, and M. Wegener, Coherent control
of electron-LO-phonon scattering in bulk GaAs, Phys. Rev. Lett. 80, 1992
(1998); D.Steinbach, G. Kocherscheiddt, M. U. Wehner, H.Kalt, and M.Wegener,
Electron-phonon quantum kinetics in the strong-coupling regime, Phys. Rev.
B 60, 12079 (1999)
We present a detailed analysis of electron and hole dynamics in simple (Al) and noble (Cu, Ag, and Au) metals, by means of first-principles many-body calculations. Quasiparticle damping rates are evaluated from the knowledge of the electron self-energy, which we compute within the GW approximation of many-body theory. Inelastic lifetimes are then obtained along various directions of the electron wave vector, with full inclusion of the band structure of the solid. Average lifetimes are also reported, as a function of the electron energy. In Al, splitting of the band structure over the Fermi level yields electron lietimes that are smaller than those of electrons in a free-electron gas. In the noble metals, a major contribution from d electrons participating in the screening of electron-electron interactions yields electron lifetimes that are above those of electrons in a free-electron gas with the electron density equal to that of valence electrons. While holes in a free-electron gas are known to live shorter than electrons with the same excitation energy, our results indicate that $d$-holes in noble metals exhibit longer inelastic lifetimes than excited $sp$-electrons, in agreement with experiment.
References:
[1] I. Campillo, J. M. Pitarke, A. Rubio, E. Zarate, and P. M. Echenique, Phys. Rev. Lett. {\bf 83}, 2230 (1999).
[2] I. Campillo, V. M. Silkin, J. M. Pitarke, E. V. Chulkov, A. Rubio, and P. M. Echenique, Phys. Rev. B {\bf 61}, 13484 (2000).
Adsorption of molecules on silicon surfaces is a very active research field. This interest is motivated by their technological importance in microelectronic device manufacturing, but also by the fundamental interest on the interaction of molecules with the dangling bond states of semiconductor surfaces. One typical example is the adsorption of the ethylene (C$_2$H$_4$) molecule on the Si(001) surface which is particularly important for diamond film growth, and formation of silicon carbide on crystalline silicon.
In a very recent angle-resolved photoemission study of C$_2$H$_4$ on single-domain Si(001)-2$\times$1 using synchrotron radiation, the electronic structure of the adsorption system has been investigated in detail [1] allowing to identify seven ethylene-derived peaks. Two of these states, $1b_{3u}$ and $1b_{2g}$, were found to delocalize along the Si-Si dimer rows while they are localized in the direction perpendicular to the rows. In connection with this study, a calculation of the electronic structure has also been carried out [2] within the local-density approximation (LDA) to DFT showing a qualitative agreement with experiment: the 1D-dispersion features of the $1b_{3u}$ and $1b_{2g}$ states are well-reproduced. But, {\it the absolute energies of the adsorbate states are systematically shifted up with respect to the substrate states}.
By performing a careful analysis of the STM images obtained for various coverages of the C$_2$H$_4$/Si(001) surface [3], it was found that the C$_2$H$_4$ molecules appear slightly darker than the bare silicon dimers when tunneling out of the surface (i.e. the STM tip moves lower in order to maintain the same tunneling current). This can only be understood in terms of electronic structure effects. Following up this study, STM images were computed within DFT-LDA for a semi-covered surface [4]. In clear contradiction with experiments, the isolated molecules were found to appear brighter than the bare dimers. However, the experimental contrast could be recovered by taking into account the influence of the tip-induced electric field.
The theoretical studies mentioned above [2,4] rely on the electronic band structure obtained within the DFT. However, there is no formal relation between the Kohn-Sham eigenvalues and the electron excitation spectra, which can therefore can be significantly different. In this work, we present a study of the electronic properties of the C$_2$H$_4$/Si(001) surface using an accurate many-body formalism within a quasiparticle approach. The calculations are performed within the $GW$ approximation [5] which has been shown to yield quasiparticle energies within 0.1-0.2 eV as compared to photoemission experimental data for bulk crystals [6] and surfaces [7]. Here, for the first time to our knowledge, we investigate the capability of the $GW$ approximation to describe the electronic energy levels of molecular adsorbates on semiconductor surfaces.
On the one hand, we investigate the fully-covered surface. We show that the quasiparticle band structure is in an excellent agreement with photoemission spectra. The self-energy corrections for the adsorbate states are found to be about 1.5 eV larger than those for the bulk states, demonstrating the dependence of the self-energy correction on the localization of the wavefunctions. On the other hand, we also consider the semi-covered surface. By extrapolating the self-energy correction taking the localization into account, we compute $GW$ corrected STM images and show that the contrast between the bare Si dimers and the C$_2$H$_4$ molecule is significantly improved with respect to DFT-LDA.
[1] W. Widdra, {\it et al.}, Phys. Rev. Lett. {\bf 80}, 4269 (1998).
[2] U. Birkenheuer, {\it et al.}, J. Chem .Phys. {\bf 108}, 9868 (1998).
[3] A. J. Mayne, {\it et al.}, Surf. Sci. {\bf 284}, 247 (1993).
[4] H. Ness, A. J. Fisher, and G. A. D. Briggs, Surf. Sci. {\bf 380}, L479 (1997); H. Ness and A. J. Fisher, J. Phys.: Condens. Matter {\bf 9}, 1793 (1997); H. Ness and A. J. Fisher, Phys. Rev. B {\bf 55}, 10081 (1997).
[5] L. Hedin, Phys. Rev. {\bf 139}, A796 (1965); L. Hedin and S. Lundqvist, Solid State Phys. {\bf 23}, 1 (1969).
[6] M. S. Hybertsen and S. G. Louie, Phys. Rev. Lett. {\bf 55}, 1418 (1985); Phys. Rev. B {\bf 32}, 7005 (1985); Phys. Rev. B {\bf 34}, 5390 (1986); R. W. Godby, M. Schl\"uter, and L. J. Sham, Phys. Rev. Lett. {\bf 56}, 2415 (1986). Phys. Rev. B {\bf 37}, 10159 (1988).
[7] X.Blase, X. Zhu, S. G. Louie, Phys. Rev. B {\bf 49}, 4973 (1994);
M. Rohlfing, P. Kr\"uger, J.Pollmann, Phys. Rev. B {\bf 52}, 1905 (1995);
O. Pulci, G. Onida, R. Del Sole, and L. Reining, Phys. Rev. Lett. {\bf
81}, 5374 (1998).
The significance of quantum dots for new physical insight on the nanoscale and future technical applications has long been recognised. As small quantum dots of nanometre size have moved into the realm of experimental feasibility, theory has yet to provide a comprehensive understanding of their underlying physics.
In contrast to a wide range of phenomena in quantum dots, image effects have not been intensively studied theoretically. Many-body effects in particular are aggravating accurate theoretical approaches. Based on a more qualitative and classical analysis of image effects [1], we pursue an approach by Saito {\it et al} [2] to apply the $GW$ method to spherical jellium clusters. We developed a spherically symmetric formalism for the self-energy corrections, in which the dynamical screening of the Coulomb interaction includes these classical image effects, to testify the hypothesis proposed in [1]. An overall shift in the quasiparticle eigenvalues is observed, together with relative alterations in the energy spectrum, both of which are inherently absent in other methods such as density-functional theory. The work will subsequently be extended to fully realistic quantum dots.
[1] Patrick Rinke and R. W. Godby, MSc dissertation: {\it Image Effects in Quantum Dots} (1999)
[2] Susumu Saito, S. B. Zhang, Steven G. Louie, and Marvin L. Cohen
Phys. Rev. B {\bf 40} 3633 (1989)
The total energy surface (in particular, the resulting geometric equilibrium structure) of an excited electronic state is generally different from that of the ground state. The system will thus observe structural relaxation while being excited. Concomitantly, vibrational side bands will show up in the optical spectra. Such effects are discussed here for molecules and for the surface exciton at the Si(111)-(2x1) surface. The transition into the excited state is described by ab-initio techniques, including GW quasiparticle corrections and excitonic binding energies due to the electron-hole interaction.
The spatial extension and binding energy of excitons in
semiconducting conjugated polymers is still the subject of intense debate.
We address this problem through first-principles calculations
(within DFT, plane-waves and ab-initio pseudopotentials),
which allow to include electron-hole correlation effects
in a fully 3D approach through the density-matrix formalism.
We show results for the correlated optical spectrum and the exciton
wavefunctions of single-chain and crystal
poly({\em para})phenylene-vinylene (PPV).
We present ``ab-initio" FLAPW(a) calculations on N--terminated [001] ordered GaN/Ag and GaN/Au interfaces. Our results show that the density of gap states is appreciable only in the first semiconductor layer closer to the interface. The gap states decay length in the semiconductor side is about 3.8 a.u. and is independent on the deposited metal, therefore being to a good extent a bulk property of GaN. Our calculated values of the Schottky barrier heights for GaN/Ag and GaN/Au are respectevely 0.87 eV and 1.08 eV. Both these values are smaller than the GaN/Al(b) value 1.51 eV and this quite large spread of values excludes the possibility of a Fermi level pinning within the gap. This quite large variations of the Schottky barrier height as a function of the metal, in contrast with the behavior of GaAs/metal interfaces, are explained by the dependence of potential barrier on the structural arrangment of the first metal layer at the interface due to the low screening of GaN compared to GaAs.
(a)H.J.F. Jansen and A.J. Freeman Phys Rev B Vol. 30, 561 (1984) (b)S.
Picozzi, A. Continenza, S. Massidda and A.J. Freman Phys Rev B Vol. 55,
4849 (1998)
The decay properties of the one-particle Green function in real space
and imaginary time are systematically studied for solids. I present an
analytic solution for the homogeneous electron gas at finite and at zero
temperature as well as asymptotic formulas for real metals and insulators
that allow an analytic treatment in electronic-structure calculations based
on a space-time representation. The generic dependence of the decay constants
on known system parameters is used to compare the scaling of reciprocal-space
algorithms for the GW approximation and the space-time method.
WWW home page: www.fhi-berlin.mpg.de/th/member/schindlmayr_a.html
Optical spectroscopy of surfaces, in particular
reflectance anisotropy spectroscopy (RAS) is a powerful
and extremely versatile tool for {\em in situ} control of semiconductor
processing with real-time feedback. The understanding and interpretation
of the measured spectra, however, has been hampered by relatively
slow theoretical progress.
We demonstrate that even for complex surface structures such as InP growth planes [1] and one-dimensional defects on Si surfaces [2] quantitative agreement between {\em first principles} calculations and experiment is possible, provided the calculations are numerically converged and self-energy corrections are included. Our calculations are done within DFT-LDA, using a massively parallel, real-space multigrid technique [3] to cope with the large supercells and many electronic states needed to calculate the surface dielectric function. Quasi-particle corrections are applied using a simplified GW scheme [4] or a scissors operator approach. We identify two distinct sources for the optical anisotropy: (i) highly structure-dependent features are caused by transitions involving electronic surface states, and (ii) derivative-like oscillations or peaks at the bulk critical point energies arise from transitions between surface-modified bulk wave functions. Two mechanisms cause anisotropy signals from layers beneath the surface: the influence of the anisotropic surface potential on the bulk wave functions as well as minor contributions from atomic relaxations caused by surface-induced stress.
[1] WG Schmidt {\em et al.} Phys. Rev. B {\bf 61}, R16335 (2000).
[2] WG Schmidt, J Bernholc, Phys. Rev. B 61, 7604 (2000); WG Schmidt, F Bechstedt, J Bernholc, submitted to Phys. Rev. B.
[3] EL Briggs, DJ Sullivan, J Bernholc, Phys. Rev. B {\bf 54}, 14362 (1996).
[4] F Bechstedt, R Del Sole, G Cappellini, L Reining, Solid State Commun. {\bf 84}, 765 (1992).
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