Session N7: Recent Advances in the Computation of Optical and Transport Properties of Nanostructures

Optical Properties of Nano-Crystallites

The optical properties of nanostructured materials are interesting due to the tunability of the electronic structure, of the lifetimes, and of the excitation spectra. This calls for precise knowledge of the physical effects which create the desired properties. Thereby it is of utmost importance to settle the question as to how many-body effects have to be incorporated in the description of the excitation aspects inherent in any optical process. \\ Static DFT-LDA \textit{ab initio} calculations have now become possible for systems of about 1000 atoms for the ground state. Time-dependent DFT (TDDFT) can in principle describe excitations as exhibited in optical spectra. However, approximations for the exchange and correlation contributions that are valid in a wide range of situations and efficient enough to be applied to large nanostructures are still to be found. GW calculations deal only with charged (electron addition and removal) excitations. The solution of the Bethe-Salpeter equation (BSE) gives good answers for neutral excitations like absorption but is numerically heavy and so far tractable for rather small systems only.\\ In my talk I will briefly review the state of the calculation of optical properties. Using bulk semiconductors and Ge, Si, and alloy nanocrystals as illustrations, I will then discuss the following points: \begin{itemize} \item Manifestation of confinement effects in various spectra; \item Importance of surface effects; \item Interplay between many-body effects and confinement and surface effects; \item Importance of short- and long-range contributions. How are they adequately described? (Important, e.g., for embedded nanostructures.) \end{itemize} These questions will be discussed in view of the optical properties, but also for loss spectra and photo-emission. Methods used are DFT-LDA, TDDFT in various approximations, GW, and BSE.   

Atomistic Pseudopotential Calculations of the Electronic and Optical Properties of Self-Assembled Quantum Dots

The optical spectrum and the charging energies of semiconductor quantum dots have been recently measured with high accuracy. Both of these experimental techniques probe many-body states that are not directly described by independent particle theories such as the density functional theory. On the other hand, quasi- particle theories that can in principle address the problem, such as GW, are computationally too demanding for the study of nanostructures (as opposed to clusters) where many thousands of atoms are involved. One way to approach this problem is to use the effective mass approximation or the k.p method and choose a confinement potential that reproduces a few known experimental facts (e.g. the splitting between confined levels). These methods can provide a good initial guess but were shown to be too crude to enable a quantitative comparision with recent experiments. We therefore adopt a bottom-up atomistic approach where instead of starting from a simplified approach, such as effective mass, and progressively increase the complexity by adding parameters, we start from the accurate atomistic description (LDA or GW) and work ourselves up using a few well controlled approximations.\\ I will first present the method, namely (i) the scheme that is used to derive the empirical pseudopotentials including the piezoelectric effect, (ii) the choices that have to be made for the basis used to expand the wave functions, (iii) the inclusion of corelations through Bethe-Salpeter-like treatment. I will then present recent applications of the theory to calculate the fine-structure [1] of excitons and charged excitons, the charging spectra of holes [2] and the degree or entanglement stored in a quantum dot molecule [3].\newline \newline [1] G. Bester, S.V. Nair, A. Zunger, prb {\bf 67}, 161306 (2003). \newline [2] L. He, G. Bester, A. Zunger, PRL (in press). \newline [3] G. Bester, J. Shumway, A. Zunger, PRL {\bf 93}, 047401 (2004)   

Density Functional Theory of the electrical conductivity of molecular devices

The theoretical modeling of electrical transport through nanoscale devices is a very challenging task: On one hand, the conduction properties of a molecular junction depend crucially on details of the chemical bonding, particularly at the interface. Such properties are routinely studied using methods based on density-functional theory (DFT). On the other hand, ground-state theories like DFT cannot be directly applied to systems with a finite current, because such devices are out of equilibrium. One possibility to overcome this problem is to study electron transport in the time domain. In the spirit of what is done in semiclassical Boltzmann approaches, one considers the system subject to both an external electrical field and to dissipation due to inelastic scattering. The combined influence of the external driving force and dissipation leads to a steady state with finite current. In this presentation I will first show how time-dependent DFT can be formally extended to dissipative systems, described by a Liouville master equation for the reduced density matrix. In a second step this formalism is then applied to calculate the current-voltage characteristics of molecular junctions, like e.g. carbon nanotubes suspended between metallic contacts.   

Self-interaction errors in density functional calculations of electronic transport

All density functional (DFT) calculations of single-molecule transport to date have used continuous exchange-correlation approximations, such as the local density approximation (LDA) or the generalized gradient approximation (GGA). These usually provide a good description of metallic systems, but fail in predicting the correct I-V curve for molecules weakly coupled to the current/voltage probes. Most of the problem can be attributed to the lack of the derivative discontinuity of the DFT potential in local approximations. These in fact continuously connect the orbital levels for different integer occupations, leading to qualitative errors such as the erroneous prediction of the dissociation of heteronuclear molecules into fractionally charged ions In this talk I will first describe the typical errors arising from neglecting the derivative discontinuity in transport calculations [1], namely the erroneous prediction of metallic transport for insulating molecules. Then I will present a simple and computationally undemanding atomic self-interaction correction scheme for transport. This preserves the computational and conceptual simplicity of standard LDA, and nevertheless re-introduces part of the derivative discontinuity. The method is implemented in our quantum transport code Smeagol [2] (www. smeagol.tcd.ie) and several examples will be given. \newline \newline [1] C.Toher, A.Filippetti, S.Sanvito, and K.Burke, Phys. Rev. Lett. 95, 146402, (2005). \newline [2] A.R.Rocha, V.M.Garcia Suarez, S.W.Bailey, C.J.Lambert, J.Ferrer, and S.Sanvito, cond-mat/0510083   

Electron-vibration interaction in molecular electronics and GW approximation for the e-e interaction in transport theory

The field of molecular electronics has seen a tremendous expansion in recent years, thanks to the realization of ingenious experimental setups and the fundamental achievement of reproducible results and behaviours. Significant progresses have also been made from a theoretical point of view, although the agreement with experiments is still not satisfactory. The challenges for a complete understanding of transport in such systems are still considerable. Inelastic electron tunnelling spectroscopy is becoming very popular in the field thanks to its powerful capability of probing molecular vibrational properties and could provide in the future a valuable characterization tool if correctly related to theoretical calculations. We simulate IETS spectra of various molecules between metal contacts and show the importance of such simulation for the interpretation of the experiments. Particular attention is devoted to the evaluation of Joule heating and thermal dissipation. The problem is tackled within the formalism of NEGF by the calculation of appropriate electron-phonon self-energies. The electron-phonon coupling is derived from the DFTB Hamiltonian. The Power dissipated is calculated from the virtual contact current originated from phonon emission and absorption processes. Preliminary results of thermal dissipations of molecules coupled to Au and Si substrates will be shown. As well known, all DFT methods tend to underestimate the electronic band-gap of semiconducting and insulating materials. In particular the band-gap of conjugated organic molecules is usually underestimated by few electronvolts. However, band-gap corrections are crucial for quantitatively correct calculations of the tunneling current through organic molecules. We show a novel implementation of the \textit{GW} correction applied to our DFTB method and show its applications to molecular systems sandwitched in-between electrodes to obtain a first-principle correction of the $e-e$ interaction energy. The resulting self-energy is used to improve the system \textit{GF} and to obtain a correction of the tunneling current. We also apply the \textit{GW} correction in the context of the computation of the complex band-structures of polymers such as poly-acetylene or poly-phenylene and show how the energy gap and decay lengths of the evanescent states should be corrected by quasi-particle effects.