1. 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

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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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
Eg(0)
Eg(F)
Eg(L)
April 03, 2009
Fabio Trani - HPC in Materials Science

17. 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

18. 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