Andrea Marini Talking about my ( ) : theory, applications and challenges

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Presentation transcript:

Andrea Marini Talking about my ( ) : theory, applications and challenges Ferrari 360 “Modena” Cilindrata: 3600 Cm3, Cilindri: 8 a V Trazione: posteriore, Motore: posteriore longitudinale Velocita' max: 300 km/h, Potenza max: 400 CV CNR-INFM National Research Center, Modena, 23/01/2007

My ( )? Developers & Users Users

Performance: 200 Atoms 160 Gb BS matrices extensive parallelization Available on Subversion Repository Building 1: Direction, C command line, on-fly variables selection Building 2: GW (plasmon pole and real axis) Building 3: Bethe-Salpeter Building 4: TDDFT, linear response, ALDA (reciprocal and real space) and beyond Building 5: Total energy, ACFDT Project Building 6: DFT, OEP and Generalize Kohn-Sham Project Building 7: BSE, Cut-Offed Hartree Potential Project Building 8: Collinear and not collinear SPIN extension Project Building 10: Surface EELS and RAS Project Building 9: Electron Phonon interaction (Finite temperature formalism)

Detector modelling Kinematics & scattering Real space spectral decomposition Surface geometry analysis Standard & advanced models of loss function Real space dielectric functions Surface Spectroscopy SELF Modules Reflection Anisotropy Spectroscopy (RAS) Reflection Electron Energy Loss Spectroscopy (REELS) GaAs(001)-c(4x4) Computation of reflection electron energy loss via integration of slab dielectric function in real space: (q-dependent, spatial dependence)

Density Functional Theory (E xc ) The Adiabatic Connection Fluctuation Dissipation theory Covalent bonds coexist with van der Waals forces Small energy differences GGA (like EXX/LDA) fails h-BN Structure of layered materials: interesting case AM, P. Garcia Gonzalez, A. Rubio; PRL 96, (2006) LDA underbinds the layersbut works gret near equilibrium distance

AM, P. Garcia Gonzalez, A. Rubio; PRL 96, (2006) Density Functional Theory (E xc ) h-BN Fluctuation-Dissipation Theorem Exchange and correlation must be treated at the same level (GGA, EXX + LDA/GGA will not work) Adiabatic-Connection FDT functional (ACFDT):

Density Functional Theory (V xc ) The band-gap problem ● In theory: KS band gap differs from energy gap ● In practice: LDA 30-50% too small EXX depends on the system Hybrids/SX” promising results

Density Functional Theory (V xc ) Beyond LDA (OEP) What is the effect of long range correlation? Niquet et al. PRB 70, (04) Optimized effective potential method M. Grüning, AM and A. Rubio JCP124, (06) By adding it to the EXX+RPA band gap the we get good band gap Calculated derivative discontinuity: 30-50% of the band gap

Density Functional Theory (V xc ) Beyond LDA (GKS) What is the effect of the spatial nonlocality? Seidl et al. PRB 53, 3764(96) Generalized Kohn-Sham method Does it exist a LOCAL OEP potential that yields the correct band-gap ? Non locality is crucial to reduce the derivative discontinuity M. Grüning, AM, and A. Rubio PRB 74, (R) (06)

Density Functional Theory (f xc ) The exciton problem Onida, Reining and Rubio, Rev. Mod. Phys. 74, 601 (2002) Exact-Exchange Kim Gorling, PRL 89, Many-Body functionals. Sham Schluter, PRL 51, 1888; Tokatly Pankratov PRL ; Many-Body functionals a la' TDDFT, Ulf von Barth, PRB 72, (2005). The “Response function” approach”, Reining, Olevano, Rubio, Onida PRL 88, Sottile, Olevano, Reining, PRL 91,

Hp. (1) Hp. (2) AM, R. Del Sole, Phys. Rev. Lett., 91, (2003). The polarization function approach

BSE TDDFT Experiment QP-RPA Density Functional Theory (f xc ): Bound excitons Resonant Causa l AM, R. Del Sole, Phys. Rev. Lett., 91, (2003).

SELF and the Many-Body World QUASIPARTICLES Energy Levels: PRL 88, Lifetimes: PRB 66, (R) EXCITONS Memory Effects: PRL, 91, Complex Materials: PRL 94, (2005), PRL 96, (2006), PRL 98, (2007).

light The polarization function: a two body problem S(tatic)BSE The BSE is not solvable in the space of single-time Green's functions Static approximation for W(t) AM, R. Del Sole PRL, 91, (2003)

S(tatic)BSE The BSE: a O(NxN) problem Haydock Recursive Method to calculate PRB, 67, (2003)

Si H H Y. Borenzstein et al. PRL 2005 M.Palummo, AM, et al., in preparation Surfaces: Si(100) and C(100)2x x Bethe-Salpeter Hamiltonian (160 Gb disk space) Surface exciton with 1 eV, binding energy. The strongest ever observed for semiconductor surfaces Crucial excitonic effects below and above the surface gap (4 eV). The neglection of excitonic effects leads to a RAS qualitatively and quantitatively wrong. C(100) Surface: M. Palummo, O. Pulci, R. Del Sole, AM, et al., Phys. Rev. Lett., 94, (2005).

Intrigiung (but efficent) cancellation of the excitonic and quasiparticle gap correction. L. Wirtz, AM, A. Rubio, PRL 96, (2006) The strong exciton localization dictates the fast convergence of its binding energy to the sheet value. Strong exciton localization. The absolute position of the 1st excitonic peak is almost independent of the tube radius. BN nanotubes: dimensionality effects

From Si Nanowires to porous Silicon M. Bruno, M. Palummo, AM, R. Del Sole, S. Ossicini Phys. Rev. Lett. 98, (2007). PS modelized using a gaussian distribution of Si nanowires. Clear difference between the measured optical and the GW QP gaps. Crucial excitonic effects. Size and orientation dependent self-energy corrections. Huge excitonic effects (reduced dimensionality).

“ SELF, a shiny pot of fun and happiness” [C. Hogan]