Vladan Mlinar tells Journal of Materials Chemistry about his hot paper.

1. Can you briefly describe what you achieved in this article? 
This paper has two main contributions. First, we provide an elegant, three-dimensional model for studying electronic and optical properties of self-assembled quantum dots (QDs) and quantum dot molecules (QDMs) grown on high-index planes and placed in an external magnetic or electric field. Size, shape, and composition profile of a model QD and/or QDM as they enter our calculations are extracted from structural characterization e.g. by cross-sectional STM.  Our theoretical approach takes into account strain distribution in and around the dots, effects of piezoelectricity, and band nonparabolicity. Also, we point out some very important stumbling blocks in the numerical implementation, such as breaking of the gauge invariance of discretized Hamiltonian, diagonalization of large sparse matrices, etc. Second, we analyze the role of piezoelectricity of QDs grown on [11k] substrates, where k=1,2,.,9 and QDMs containing eight laterally and vertically coupled QDs, grown on [11l], where l=1,2,3. We predict variation of the transition energies of the QDM as a function of substrate orientation and inter-dot distances in the molecule.

2. Could you explain the significance of your article to the non-specialist? 
In practice, manipulation of the QD's electronic and optical properties has been realized through a variation of the QD growth conditions, e.g. growth temperature, growth on high index planes, or by exploiting the effect of nano-capillarity on nonplanar surfaces to grow QDs on a prescribed position on the substrate, to apply post-growth procedures such as thermal or laser annealing. Our detailed theoretical model is able, on the one hand, to include all the variation of the input structure as demanded by the experiment and on the other hand, to give fast and reliable output on the electronic properties. We presented details on the implementation of such a theoretical model that includes effects of strain and piezoelectric fields, growth on high index planes, band nonparabolicity, Coulomb interaction between carriers, and effect of an external tilted magnetic field. Furthermore, we show variation of the piezoelectric field with substrate orientation of QDs and QDMs, as was not done previously, as well as predict variation of the optical transition energies with the substrate orientation.

3. What has motivated you to conduct this work? 
A multitude of current and potential applications of quantum dots require a deeper understanding of the quantum dot electronic structure, not only on the qualitative but also on the quantitative level. Results of our model are detailed enough for it to allow quantitative comparison with experimental data. Recent increased interest in QD growth on high index planes has been shown to be useful, since it brings about several practical advantages such as good quality QD structures with high densities and low size dispersion. It also enables 3D growth ranging from a chainlike pattern to a square lattice of QDs. Interesting physics of QDs grown on high-index plane as compared to well investigated [001] grown QDs should arise from the fact that different substrate orientations result in different planar projections of the conduction and valence bands of the constituent crystals forming the QDs. Therefore, it is of fundamental importance to understand the underlying physical features of such a system. How are the electronic structure and transition energy influenced by the substrate orientation? What are the main differences with the well investigated [001] grown QDs and QDMs? Those are just two questions we answer in the presented study.

4. Where do you see this work developing in the future? 
The model presented is sufficient to describe photoluminescence and magnetophotoluminescence measurements performed both on an ensemble of QDs and on a single QD.  Currently, we are able to model self-assembled QDs made of III-V zinc-blende direct gap semiconductors, where the minimum of the conduction band and maximum of the valence band (if we neglect linear k terms) are at the ? point. Extension of the model to include a more precise description of the band diagram of the whole Brillouin zone, as well as to calculate exciton complexes, would give a powerful tool to cover a wide range of experiments in the area of semiconductor nanostructures.

5. Are there any particular challenges facing future research in this area? 
A "complete" understanding of the nanoworld - with the aim of producing novel optoelectronic devices, enabling a breakthrough in modern photonic technologies - is still pending. From the experimental point of view, fabrication of highly ordered QD configurations (by exploiting a profound understanding of the formation processes) is one of the primary areas of interest, and in general would lead to the construction of QD superlattices, creating QD solids, or integration of QD systems into photonic crystal cavities or in waveguides. Theoretical modelling should follow these experimental developments, providing an understanding of the electronic states in coupled QDMs, and QD superlattices, exciton and photon entanglement in those systems, identification of the results of optical spectroscopy performed on such QD systems, exciton complexes, and the effects of external electric and magnetic fields.

Vladan Mlinar (left) graduated from the department of Physical Electronics, University of Belgrade (Serbia) in 2002. In the period 2002-2003 he was a research assistant at the Laboratory of Atomic Physics at the Vinca Institute of Nuclear Sciences (Belgrade, Serbia). Since autumn 2003 he has been working in the Condensed Matter Theory group headed by Professor Dr François Peeters at the University of Antwerp, and was a visiting researcher at the Technische Universität Berlin (Berlin, Germany) in 2005. He received his PhD degree in 2007. His research interests are the modeling of the electronic and optical properties of semiconductor and graphene based nanostructures. He is the author of the 3D numerical code which solves the strain-dependent Schrödinger equation in eight-band k.p theory, taking into account the influence of substrate orientation and effects of an external tilted magnetic field.

François Peeters is full Professor at the Department of Physics at the University of Antwerp (Belgium) and head of the research group "Condensed Matter Theory". He obtained his PhD in 1982, and was a postdoctoral researcher at Bell Laboratories (Murray Hill, NJ, USA) and Bell Communications Research (Red Bank, NJ, USA). He has been visiting professor at the University of Notre Dame (IN, USA), Universidade de São Paulo (São Carlos, Brasil), The Clarendon Laboratory (Oxford, UK), the Australian National University (Canberra, Australia) and the Max-Plank-Institut für Physik Komplexes Systeme (Dresden, Germany). His research interests are the modeling of mesoscopic and nanophysics of semiconductors, superconductors and hybrid structures.