Nanotechnology for fast DNA sequencing

One of the great scientific and technological problems of today is understanding the structure and function of DNA and closely related development of inexpensive methods for DNA sequencing. The latter promises to revolutionize both our understanding of DNA as well as significantly advance personalized medicine. Two aspects of the problem that are currently being investigated are non-covalent interactions and non-equilibrium electronic transport properties at nanometer scale. Non-covalent interactions are known to play an important role in biochemistry, notably the Hydrogen-bonding that pairs nucleotides in the double helix of DNA, as well as stacking interactions of DNA strands or surface-adsorbed nucleotides, which we study using the numerical simulation based on the density function theory (DFT). Our main research activity in this area is theoretical understanding of the promising approach to the fast DNA sequencing via measurement of the transverse electronic current while a single-strand of DNA is passing through a nanopore equipped with nano-electrodes, where the task is to decode the nucleotide sequence based on the measured current. Since the main electronic transport mechanism is tunneling, it is advantageous to apply large biases to increase the current, and the correct theoretical modeling of such experimental setups requires use of non-equilibrium transport, which we study using DFT in combination with the Kelydish Green's function formalism.

Photovoltaics

An important area of applied physics today is development of novel as well as improvement of current solar-cell technologies, characterized by the efficiency of material in converting the light into electrical current. The most efficient in this respect are (poly)crystalline and amorphous Silicon based photovoltaics. Among the most promising alternatives are those based on TiO2, and our research is oriented towards studying electronic structure of physically as well as chemically modified different phases of TiO2, using numerical DFT simulations to better understand results of experimental measurements. The second direction of our research is concerned with the dominant mechanism of the photon conversion into electrical current via creation and transport of excitons formed after the photon capture in optoelectric materials. Efficacy of photovoltaics is determined to a large extent by the life-time and dynamics of excitons, and our current research activities are also oriented towards a better understanding of the exciton dynamics with the perspective of material design with higher exciton to electron transfer rates upon the photon capture, using numerical modeling of Markov processes describing the exciton dynamics.

Quantum-mechanical disordered and chaotic systems

Since the discovery of the Anderson localization, one of the main problems of the theory of disordered systems was theoretical understanding of the transition from the insulating localized phase of strongly disordered conductors to the metallic delocalized phase of weakly disordered conductors, its nature, universal properties and transport mechanisms. In this respect the first area of research is the development of the scaling theory of the Anderson metal-insulator transition, using numerical simulations and applying the renormalization-group formalism. An important class of the disordered systems are 2d Anderson models with chiral symmetry, most notably the random-flux and the random-bond Anderson models. They appear in certain effective theoretical descriptions of high-Tc superconductivity as well as quantum-Hall effect. Their main property is the appearance of non-localized states at the band center, in contradistinction to the 2d Anderson model where all electronic states are at most exponentially localized, and properties of these exceptional states remain in focus of the second area of the ongoing research. Third area is statistical properties of disordered conductors, which are by large governed by the random-matrix theory and the related notion of quantum chaos. Notably, the far tail of distribution of electronic eigenstate intensities of mesoscopic metallic grains are determined by the rare realizations of the disorder, which proper understanding remains a difficult problem in the theory of disordered and quantum-chaotic system.

Quasicrystals

This year's Nobel prize for Chemistry was awarded for the experimental discovery of quasicrystals, strange materials whose X-ray diffractometry shows from the physics viewpoint crystalographically impossible symmetries. Those are rapidly cooled alloys exhibiting unusual diffraction patterns: five-fold in the case of Al-Mn and Al-Fe, twelve-fold in the case of Ni-Cr grains, as well as eight-fold in the case of V-Ni-Si and V-Ni-Cr thin films. The puzzle was explained by (mathematically long-known) quasicrystaline arrangements of atoms, where each set of atoms of the material repeats indefinitely throughout the crystal, sometimes with rotational symmetry and always without the presence of translational symmetry. Such arrangements of atoms can be obtained mathematically by tiling of plane or space with a finite number of specially chosen tiles, from recursive rewrite systems, or by projecting translationally symmetric lattices in higher dimensional spaces onto 3d hyperplanes. Quasicrystals are weakly conducting, exhibiting remarkable spectral and transport properties such as singular-continuous spectrum and anomalous diffusion. In these respects, as well as in the sense that they are only partly symmetric, quasicrystals are intermediates between periodic crystals and amorphous solids.

High-performance scientific programming

Growth in applicability of numerical methods in modern science is by large driven by the rapid increase in computational capabilities of hardware due to multi-core processors, connecting of computational units via fast networks as well as rapidly increasing capabilities of graphical processing units. An efficient use of such a variety of hardware resources still remains difficult from the viewpoint of software, underlying the necessity for development of a next-generation programming languages that will allow an efficient high-level abstraction of hardware while allowing fast development of efficient parallel and correct programs for use in computational physics, chemistry and biology. In this context our research is directed towards development of high-level array-oriented parallel language of the APL family with features of modern purely functional programming languages, by utilizing programming techniques of Haskell programming language and category theory.