http://www.fisica.uniroma2.it/~mariniAndrea Marini

Talking about my( ): theory, applications and challenges

http://en.wikipedia.org/wiki/Ferrari_360Ferrari 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 Atoms160 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)

3

4

5

1

2

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 slabdielectric function in

real space:(q-dependent,

spatial dependence)

Density Functional Theory (Exc)The Adiabatic Connection

Fluctuation Dissipation theory

Covalent bonds coexist with van der Waals forces

Small energy differences

GGA (like EXX/LDA) fails

h-BN

deq=6.24a.u.

Structure of layered materials: interesting case

AM, P. Garcia Gonzalez, A. Rubio; PRL 96, 136204 (2006)

LDA underbinds the layersbut works gret near equilibrium distance

AM, P. Garcia Gonzalez, A. Rubio; PRL 96, 136204 (2006)

Density Functional Theory (Exc)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 (Vxc)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 (Vxc)Beyond LDA (OEP)

What is the effect of long range correlation?

Niquet et al. PRB 70, 245115 (04)

Optimized effective potential method

M. Grüning, AM and A. Rubio JCP124, 154108 (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 (Vxc)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, 161103(R) (06)

Density Functional Theory (fxc)The exciton problem

Onida, Reining and Rubio, Rev. Mod. Phys. 74, 601 (2002)

Exact-Exchange Kim Gorling, PRL 89, 096402

Many-Body functionals . Sham Schluter, PRL 51, 1888; Tokatly Pankratov PRL 86 2078;

Many-Body functionals a la' TDDFT, Ulf von Barth, PRB 72, 235109 (2005).

The “Response function” approach”, Reining, Olevano, Rubio, Onida PRL 88, 066404. Sottile, Olevano, Reining, PRL 91, 056402.

Hp . (1)

Hp . (2)

AM, R. Del Sole, Phys. Rev. Lett., 91, 176402 (2003).

The polarization function approach

BSETDDFT Experiment

QP-RPA

`

Density Functional Theory (fxc):Bound excitons

Resonant

Causal

AM, R. Del Sole, Phys. Rev. Lett., 91, 176402 (2003).

SELF and the Many-Body World

QUASIPARTICLESEnergy Levels: PRL 88, 016403

Lifetimes: PRB 66, 161104(R)

EXCITONSMemory Effects: PRL, 91, 256402

Complex Materials: PRL 94, 087404 (2005), PRL 96, 126104 (2006), PRL 98,

036807 (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, 25640

(2003)

S(tatic)BSE

The BSE: a O(NxN) problem

Haydock Recursive Method to calculate G0

G0 ≡⟨u0∣−H−1∣u0⟩

PRB, 67, 085307 (2003)

b3a2

b1=∥H−a0 u0∥1/2

u1=H−a0/b1 u0

a1=⟨u1∣H∣u1⟩

a0=⟨u0∣H∣u0 ⟩b0=0

Gn=[−an−bn12 Gn1 ]−1

b2=∥H−a1 u1−b1 u0∥1/2

u2=[H−a1 u1−b1 u0]/b2

a1=⟨u1∣H∣u1⟩

Si

H

Si

Si Si

H

Y. Borenzstein et al. PRL 2005M.Palummo, AM, et al., in preparation

Surfaces:Si(100) and C(100)2x1

200000x200000Bethe-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, 087404 (2005).

Intrigiung (but efficent) cancellation of the excitonic and quasiparticle gap correction.

L. Wirtz , AM, A. Rubio, PRL 96, 126104 (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 toporous Silicon

M. Bruno, M. Palummo, AM, R. Del Sole, S. Ossicini Phys. Rev. Lett. 98, 036807 (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]