Research Activities

Our group is involved in several aspects of physics of materials, although they can generally be considered under two general headings: physics of surfaces, and theory of excited states. Obviously there is quite a lot of overlap between the two.
Follow the links for a brief description of our research.

1. Surfaces and other low-dimensional systems
   • Electronic and structural properties
   • Optical properties of surfaces
   • Organic molecules on surfaces
   • 1-D systems/nanowires
   • 0-D systems/nanocristals
   • Electron energy loss at surfaces
2. Theory of excited states
   • Green's function approaches
   • Time dependent density functional theory (TDDFT)
3. Application to biological systems
4. Code development

Or, you can look at a list of recent publications.

Surfaces and other low-dimensional systems [Back to top]

Electronic and structural properties

A clear and quantitative understanding of the electronic properties of surfaces -- and their relation to the surface atomic structure -- is of fundamental importance in the development of micro- and opto-electronic devices. As technology approaches the nanoscale, understanding the properties of the semiconductor or metal surface becomes increasingly important.

DFT calculations

For many years now, Density Functional Theory (DFT) in the local density approximation (LDA) or generalized gradient approximation (GGA) has been the main tool used by theoreticians for modelling the structural and electronic properties of surfaces and interfaces from first-principles. The DFT approach is based on solution of the Kohn-Sham single particle equation:

The fourth term on the left is the exchange-correlation potential, which in principle contains all the many-body correlation effects for the ground state system.

In our group we have carried out detailed studies of the physical and electronic properties of a wide variety of technologically important surfaces, investigating various interesting properties ranging from dimer buckling on Si(100) to work functions of metal semiconductor interfaces. Below are shown results of a total energy study of hydrogen adsorption on Ru(0001); from the DFT potential energy surface we can identify the likely adsorption configurations of hydrogen.

Beyond DFT

While extremely useful for ground state calculations, DFT nonetheless yields poor agreement with experimental (inverse) photoemission data, frequently underestimating the band gaps of many semiconductors and insulators. This is often referred to as the band-gap problem, and derives from the mean-field nature of DFT and an incomplete description of many body phenomena.

The gap problem can be solved by using many-body perturbation theory (MBPT), described in more detail below. The state-of-the-art approach used to obtain quasi-particle excitation energies is to compute self-energy corrections to the DFT bandstructure within the so-called GW approximation, a first order perturbative technique. In the simplest approach, quasiparticle energies are calculated considering only the diagonal elements of the self-energy operator, and the Dyson equation is not solved self-consistently (so, strictly G_oW_o). Although apparently full of drastic approximations (and let's not even mention the word vertex), this GW flavour works well, and is now well established for bulk calculations (see Figure). We have successfully applied the approach to several surfaces (citations...), often revealing interesting physics in the process. Below we show an example of a surface bandstructure calculation, carried out within DFT and GW, on the InP(110) surface.

Sometimes, however, the original DFT band structure is sufficiently bad that even GW is not enough, and more complicated approaches are necessary to recover the experimental results. One possibility is to include the off-diagonal terms of the self-energy, by diagonalizing the self-energy operator, hence obtaining the quasiparticle wavefunctions, rather than the usual DFT ones. Such nonperturbative treatment is important for surfaces with electronic states close in energy but different with respect to their localization, such as GaAs(110) [cite/link PRB 60, 16758]. Another interesting case is the (111) surface of diamond, which is incorrectly predicted in DFT to be semi-metallic (see Figure). Due to the erroneous band occupation found by DFT, a simple opening of the gap is not sufficient, and one must try to reach a self-consistent solution of the Dyson equation, hence updating the quasiparticle energies while building the self-energy operator.

Optical properties of surfaces

Experimental characterization of materials is often obtained through spectroscopic techniques such as photoemission, inverse photoemission, electron energy loss spectroscopy and optical techniques (such as Reflectance Anisotropy Spectroscopy (RAS) and Surface Differential Reflectivity (SDR) for surfaces). It is hence very important to describe accurately the electronic excitations with highly reliable and efficient ab-initio approaches. Although DFT has proven to be a very powerful tool for electronic ground-state properties, it shows significant deviations from the experiments when excited states are involved. Presently, however, it is the only option for very large reconstructions, and insome cases it actually works well.

Small systems: excitons

The use of many-body Green's functions theory is now the state of the art to obtain optical spectra with excitonic effect included (with the solution of the two particle BSE equation) in bulk, surfaces and in nanostructures.

With regards to surfaces a recent numerical parallel implementation of an iterative algorithm (Haydock method) for solving the BSE equation, has been shown to be essential for the ab-initio calculation of optical spectra including excitonic and self-energy effects for many semiconductor surfaces where a large number of electron-hole pairs interfere and produce very large excitonic matrices which are, from a computational point of view, very difficult, if not impossible, to diagonalize.

An example of the usefulness of this method and of the need to include excitonic effects to obtain a good agreement with experimental data is given by the recent calculation of the Reflectance Anisotropy Spectrum of the (100) surface of diamond. Only the inclusion of electron-hole interactions, revealing the presence of a surface exciton with a binding energy of about 1 eV, is able to reproduce and explain the experimental spectrum (see Figure).

Intermediate systems: GW

Computation of surface optical spectra incorporating many body effects at the single particle level (i.e., using the GW-corrected electronic bandstructure, but neglecting the electron-hole interaction) have been carried out in our group for several surfaces.

These corrections are particularly important for cases when surface states and bulk states are shifted in energy by different amounts. In the Figure we show the results of one of the first ab-initio calculated RAS spectra including self-energy corrections, as carried out in our group, for the GaAs(110) surface. The comparison with experiment is improved both in the lineshape and energetic peak positions, although there are still some qualitative discrepancies. In case you haven't realized by now, RAS is really a hard quantity to calculate accurately!

Large systems: RPA+shift

Due to a fortuitous cancellation of errors between bulk and surface dielectric functions, calculating RAS spectra without rigorously including many body effects can often give good qualitative or even quantitative agreement with experiment. An approximate way to include the effects of self-energy and excitonic shifts is through the so called scissor operator approach, which in its simplest form requires a rigid shift of the DFT-LDA bandstructure. A typical shift in GaAs, for instance, is 0.5eV; this is a little smaller than the bulk GW shift of about 0.8eV.

Such a scheme is necessary for larger, computationally demanding systems, such as surfaces with large reconstructions or with a very high planewave cut off. An example where it works well is the GaAs(001)-c(4x4) surface, which was the subject of much controversy with regard to the exact atomic structure: much of the literature supports a symmetric homo-dimer (As-As) reconstruction, while newer experiments favour a heterodimer (Ga-As) terminated structure. This is in spite of the structure being thermodynamically unfavoured! Our RAS calculations are sensitive and accurate enough, however, to distinguish between the models and help support and explain the newer experimental studies (see Figure). In general, however, true quantitative agreement should require the more sophisticated approaches described above, particularly when many-body effects heavily influence the lineshape.

Organic Molecules on Surfaces

Like every other group looking for money or just interested in trying something new, we are applying our expertise in surface science towards biological systems. Much research is being carried out worldwide into technological applications of organic molecules: examples of this are for use in Organic LEDs (OLEDs), in organic sensors, or in molecular electronic circuits. We are interested in identifying and understanding the contribution of organic films towards the optical response of the molecule-solid interface, which should aid the use of optical spectroscopies in characterizing organic layers.

One of the molecules we are focussing on is pyrrole (see Figure), which is the basic constituent of porphyrin (used in nanoscale electronics) and phthalocyanine (utilized in conventional dyes, catalysis, coatings for read/write CD-ROMs and as an anti-cancer agent) molecules.

1-D systems/nanowires

The study of semiconducting nanowires is one of the most rapidly growing research areas in materials science and nanotechnology, not only from the point of view of the possible applications, but also regarding the use of the latest developments in the theory.

As well as carbon nanotubes, they have attracted an increasing scientific interest for their envisaged use in the future nanoelectronics. Their great advantage is that they are semiconductors, while the metallic or semiconducting character of nanotubes depends on their chirality which is a difficult parameter to control during the growth process. This is a very important feature for the design of nanoelectronics applications, as for instance nanotransistors, which require basic semiconductor components or in the case of photovoltaic applications. In this regard, silicon nanowires (Si-NWs) are playing a central role for their compatibility with the existing Silicon based microelectronics and have been the focus of a strong attention from the scientific community.

Beside the intense experimental work, devoted to the improvement of the NWs growth and characterization techniques and to the realization of nanodevices, an increasing number of theoretical works, based on empirical and on ab-initio approaches, is now available in the literature. The importance of the theoretical calculations is not only in the interpretation of experimental results, but also in the possibility to predict structural, electronic, optical, and transport properties to help in the realization of more efficient devices.Important progresses in the description of the electronic properties of pure and doped Si NWs have been reported, but an exhaustive understanding is still lacking. This is due, on one side to the not obvious transferability of the empirical parameters to low dimensional systems and on the other side to the deficiency of the {\it ab-initio} DFT approach in the correct evaluation of the excitation energies. In fact, due to their reduced dimensionality, the inclusion of many-body effects in the theoretical description, is mandatory for a proper interpretation of the excited state properties. In particular the quasiparticle structure is a key to the understanding of the NW charge transport as the inclusion of excitonic effects is really important for a description of their optical properties and to explain enhanced photoluminescence with respect to the bulk compounds.

Few years ago, we started to focus on this research field and we have calculated the quasi-particles (QP) and the excitonic states first of Ge-NWs and then of Si-NWs, of different orientation and size. More recently we moved to the analysis of the dependence of these physical properties on doping, surface termination and mixing.

Electron energy loss

Reflection electron energy loss spectroscopy (REELS) is a frequently exploited technique for characterizing the surfaces of metals and semiconductors. In the 1-20 eV range, where bandstructure effects are most important, spectral features are predominantly related to interband transitions and surface plasmons.

Ab-initio calculation of REELS spectra is presently made using a `three-layer' model based on a separate calculation of surface and bulk response. This is believed to perform well at low transfer momentum q, so that optical dielectric functions are often used in this case. Indeed, we have obtained results in good agreement with experiment, for the energy loss anisotropy for several GaAs(001) surfaces. With this approach we are trying to understand the changes in the loss spectra of Al(100) with coverage of pyrrole, in an attempt to explain the experimental loss spectra of its parent molecule, phthalocyanine, adsorbed on Al(100).

However, the three-layer model utilizes a spatial average over the surface layers which considerably reduces the precision. Furthermore, the reliability of the model at higher q, as needed to describe surface plasmon dispersion, is not known. Hence we have developed within the SELF code a routine which models the REELS process within a microscopic dipole scattering theory, taking into account the influence of band structure, non-locality and wave-vector dependence, via computation and integration of the inverse dielectric function in real space. This will allow us to assess the applicability of the three-layer model, as well as tackle more complex problems, such as the surface plasmon dispersion of aluminium and silver surfaces.

Theory of Excited States [Back to top]

As mentioned above, DFT is strictly valid only for the ground state of a many-electron system. Computation of excited state properties, however, is a more formidable task, requiring the use of far more complicated techniques. Although many different theoretical approaches are possible, they all must resort to the use of some reasonable approximations, the choice of which depends to some extent on the systems studied, the resources available, and the local expertise. For the systems we are most interested in, two approaches have emerged as being the most useful.

Green's function approaches

The primary methodology we use is Many Body Perturbation Theory (MBPT), in which the main building blocks are Green's functions. Green's functions make it very easy to connect the results of calculations with the observations of experiments, since they define the excited state energies exactly in terms of poles in the complex plane.

By applying perturbation theory in a suitable manner to the calculation of these functions, we are able to define approximations and formulate methods that are currently used with much success in the condensed matter field. A critical step in the development of the theory was made by Hedin in 1965, in which he showed how the self energy could be expanded in powers of the dynamically screened Coulomb potential W rather than the usual bare Coulomb potential v. This expression, in combination with related expressions for the polarization P, Green's function G, screened interaction W and vertex function yields the comprehensive set of coupled integral equations known as the Hedin equations. In principle these equations are complete; in practice, of course, we need to adopt some approximations based on physical intuition.

The GW approximation

Within MBPT, the Kohn-Sham equation above is replaced by a "quasiparticle" equation, which describes the extra hole created when an electron is extracted from the system (for example in a photoemission experiment; or, in a inverse photoemission experiment, where an electron is added to the system) and the polarization cloud that the other electrons create in order to screen it:

The quasi-particle (QP) energies are calculated solving this equation within the GW scheme, which involves the approximation with G being the single particle Green function and W the screened Coulomb interaction. This approximation comes from a first iteration of Hedin's equations. Computing the excited states energies as a first order perturbation correction to the DFT bands (perturbative GW):

A current project we are studying is the application of this scheme to the simulation of liquid water.

Beyond GW: interacting quasiparticles

The next step in the direction of increasing complexity is to include the interaction between quasiparticles. In an interacting particle-hole system (such as that immediately after the absorption of a photon) this gives rise to the excitonic effect (e-h correlation) and the local field effect (e-h exchange).

Our group was involved in the earliest fully ab-initio calculations of optical spectra that included such effects: the results are shown here for bulk silicon in the Figure. Just to show you how difficult these calculations are, consider that Hedin's equations have been about since 1965 - this calculation appeared in 1998!

Time Dependent Density Functional Theory: TDDFT

An alternative approach to the study of correlation in many-body systems is given by density-functional theory, in its static (DFT) and time dependent formulations (TDDFT). Similar to the paradigm of DFT for ground-state properties, TDDFT has emerged as a very powerful tool for the description of excited states. TDDFT is in principle exact for neutral excited-state properties, and its simplicity relies on the fact that two-point response functions are used instead of the four-point functions of Many Body Perturbation Theory.

TDDFT casts all many-body effects into the dynamical exchange-correlation kernel. Early on, it was recognized that, in extended systems, the use of the standard local density approximation (LDA) within TDDFT fails to describe, among other effects, the band--gap of insulators and semiconductors and the excitonic effects in the optical spectra. Our group is one of the leaders in developing new kernels in a Many-Body fashion and we recently achieved the description of bound states within TDDFT. The figure illustrates the success of TDDFT in describing the optical spectrum of crystalline SiO₂.

Application to biological systems [Back to top]

One of our research fields, are the electronic and optical properties of large biological systems. Some of us are focusing on an interesting class of molecules, chromophores (from Greek chromo='colour' and phore ='to beare'). These kind of compounds, are often surrounded by water molecules, ions, biological macromolecules, such as proteins, that constitute their bio-chemical environment. Chromophores absorbs and emits light in the visible or ultra-violet region generating peculiar spectral lines, which allow identification of them in their environment. In our studies, we are employing sophisticated algorithms and theoretical techniques already used to investigate mechanical, electronic and optical properties of solids and molecules. In some cases we need to improve such theories in order to treat systems with a large number of atoms, with more and more accuracy. The sophisticated theoretical techniques we use, allow us to improve our knowledge on the bio-chemical processes that rule the mechanisms of life.

Code development [Back to top]

Code development is continually being carried out in our group, most notably on the SELF code. SELF is a multi-purpose Ab-Initio Many-Body code. The main building blocks of the code are the interacting single-particle Green's functions and response functions, from which several physical quantities are derived, including quasiparticle properties (energy levels and widths), optical spectra and total energies. Different theoretical schemes are used: Bethe-Salpeter and TDDFT (two particle properties), GW and DFT (single particle properties), Adiabatic Connection Fluctuation Dissipation Theory (total energy).

More information on SELF is available by following the links at Andrea Marini's homepage.

For many years we developed our own version of the Car-Parrinello code, with the emphasis on calculation of optical properties. Development of this code has now moved with Giovanni to Milan, where it has evolved into TOSCA: Tools for the calculation of Optical Spectra and something else. More information here.

Frequently we find it necessary to perform tweaks to existing codes, for making interfaces, etc.: those we often use are listed here.