High Performance Computing in materials science from the semiempirical approaches to the many-body calculations Fabio Trani Laboratoire de Physique de la Matière Condensée et Nanostructures CNRS & Université Claude Bernard Lyon 1, France http://www-lpmcn.univ-lyon1.fr/~trani

Complexity in materials science Semiempirical methods 1000-10000 atoms Complexity of structures Complexity of materials Complexity of algorithms Density functional theory 100-1000 atoms Many-body calculations 10-100 atoms April 03, 2009 Fabio Trani - HPC in Materials Science

Complexity in materials science My experience Delafossites GW+BSE SnO2 slabs DFT Si-nc TB dimensionality number of atoms 10 100 1000 April 03, 2009 Fabio Trani - HPC in Materials Science

Semiempirical methods A proposal Objective Excitonic effects Method Tight-Binding Systems Semiconductor nanocrystals Dimensions Tens of thousands of atoms H.Hofmeister & al. Eur. Phys. J. D 9, 137 (1999) Real nanocrystal Model 3 nm April 03, 2009 Fabio Trani - HPC in Materials Science

Optical properties of Silicon Nanocrystals. Motivations Silicon nanocrystals Single particle approach Crystalline Silicon Experimental data E1 E2 E2 It is still unclear the behavior of the electron-hole interaction in nanostructures. There are extremely important, but nobody knows how the spectra change. April 03, 2009 Fabio Trani - HPC in Materials Science

Optical anisotropy in Silicon Ellipsoids Sphere = isotropy Red: independent particle calculation Black: with the surface polarization effect Elongated = anisotropy It would be extremely important to understand the role of the electron-hole interaction in the optical anisotropy of silicon ellipsoids. April 03, 2009 Fabio Trani - HPC in Materials Science

The algorithm --- 1 A few orbitals (s,p …) for each atom Interaction up to third-neighbors x Costruction and diagonalization of the single particle Hamiltonian matrix Huge sparsity, use of iterative algorithms IMPLEMENTED DURINGTHE SCOPE PROJECT April 03, 2009 Fabio Trani - HPC in Materials Science

The algorithm --- 2 Computation and inversion of the dielectric matrix Polarizability x x Dielectric matrix Screened interaction Computation and inversion of the dielectric matrix April 03, 2009 Fabio Trani - HPC in Materials Science

Fabio Trani - HPC in Materials Science The algorithm --- 3 Electron-Hole equation a Uab is the screened interaction involving pairs of transitions. To converge the calculation, many transitions have to be considered. The dynamic equation is much more complex. Costruction and diagonalization of the electron-hole Hamiltonian matrix April 03, 2009 Fabio Trani - HPC in Materials Science

Fabio Trani - HPC in Materials Science The algorithm --- 4 Oscillator strength Absorption cross section Calculation of the optical properties → sums over the transitions April 03, 2009 Fabio Trani - HPC in Materials Science

Density Functional Theory Objective Structural optimization, formation energies Method Density Functional Theory Systems Defects on metal oxide surfaces Dimensions Hundreds of atoms SnO2(110) SnO2(101) April 03, 2009 Fabio Trani - HPC in Materials Science

Density Functional Theory Defect states can be calculated SnO2 band structure and density of states, modified by the presence of oxygen vacancies. April 03, 2009 Fabio Trani - HPC in Materials Science

Density Functional Theory Surface band structures and defect levels SnO2 (101) surface bands in the stoichiometric surface (left), and modified by the presence of an oxygen vacancy (right). An excellent agreement with experimental data was found. April 03, 2009 Fabio Trani - HPC in Materials Science

Many-body calculations Objective Electronic and optical properties Method scGW+BetheSalpeter Systems Transparent conductive oxides (TCOs) Dimensions A few atoms (< 10 atoms for unit cell) Delafossites (CuMO2) are very important in solar cell technology because of their p-dopability. CuInO2 April 03, 2009 Fabio Trani - HPC in Materials Science

Fabio Trani - HPC in Materials Science scGW method Many body equation GW approximation G0W0 approximation scGW April 03, 2009 Fabio Trani - HPC in Materials Science

Fabio Trani - HPC in Materials Science GW calculations CuInO2 band structure In delafossites the d orbitals lie close to the Fermi level leading to strong correlation effects. Moreover, excitonic effects are extremely important. DFT G0W0 sc-GW Eind 0.46 1.65 3.46 Eg(0) 0.76 2.23 4.6 Eg(F) 3.32 4.2 6.42 Eg(L) 3.05 4.01 6.39 April 03, 2009 Fabio Trani - HPC in Materials Science

Fabio Trani - HPC in Materials Science Conclusions HTC is of fundamental importance in the field of Materials Science. Several problems can be exploited when computational resources are at disposal. Semiempirical, density functional or many-body approaches give the chance of studying new materials, 0- to 3-dimensional systems. April 03, 2009 Fabio Trani - HPC in Materials Science

Many-body calculations Objective From the band offset important information can be extracted on the dopability of these materials. But DFT-LDA gives wrong results April 03, 2009 Fabio Trani - HPC in Materials Science