Theory and computation of electronic excitations in condensed matter systems,

and the ETSF project G. Onida, N. Manini, L. Molinari, E. Mulazzi, A. Bordoni,

K. Gaál-Nagy, A. Incze, L. Caramella, M. Cazzaniga, E. Ponzio, and M. Gatti*

 Dipartimento di Fisica and INFM, Università di Milano*LSI-SESI,Ecole Polytechnique, Palaiseau, France

• Why excited state “ab-initio” calculations?

• Theory: State-of-the-art, and recent developements (mostly density-based)

• Examples: solids, clusters, surfaces

• The European Theoretical Spectroscopy Facility:

INFM

A initiativePosters!

H. Prinzbach et al.Nature 407, 60 (2000)

h

e-

C20

Why excited states? -Spectroscopies (experimental characterization)

RT PL excited with a He-Cd laser

500 600 700 800 9000

20

40

60

80 Vs = -50 Vs = -25 Vs = 0 Vs = 25

PL

Int

ensi

ty (

cts)

Wavelength (nm)

Photoluminescence in nc-Si:H films

c. 2.5 eV c. 0.6 eV

Why excited states? -”Useful” response to excitations (1)

Why excited states? -”Useful” response to excitations (3)

• predictivity (new esperiments, new materials)

• access to details which are difficult to obtain experimentally

• useful to design materials with the desired properties

• generality, transferability, accuracy

Why ab-initio?

“Just” solve Schroedinger equation!

• “first principles”: no parameters (ingredients: N,Z)

Layer-by-layer spectrum decomposition

C.Hogan, R. Del Sole, and G.Onida, PRB 68, 035405 (2003)

Surface optical reflectivity - study of anisotropy spectra

example: Si(100)(2x1)

Tools to analyse the calculated

spectra

ab-initio methods

• excited electronic states– C.I. (Quantum Chemistry)– Green’s functions (1965-->’80-->today)

Spectroscopy: oneneeds also the

“First principles” calculations = theory without free parameters

• ground state:– Density Functional

Theory (DFT) (1964):

(W.Kohn: Nobel prize 1998)

r1,r2,.....,rN) ?

rt) A = A [t,t]1984: TDDFT! (Runge, Gross):

Which excitations?

optical

electronic

reflectivityabsorption h

photoemission e-h

inverse photoemission he-

electron energy-loss E,q

e-

STM (I/V) e-

h

theory:

probe

• Photoemission:

One measures EQP = EN – EN-1 = poles of G

e-h

The algebraic sum of the EQP measured in photoemission and inverse photoemission yields the quasiparticle gap (Egap-QP)

QP and optical gaps coincide only when excitonic effects are negligible (Independent Quasiparticles approximation).

• Absorption: hhoptical gap

Egap-opt = E’N – EN ≠ EN+1 + EN-1 – 2EN = Egap-QP

What is an absorption spectrum?

v

c

h

Independent quasiparticles and transitions?

Im [] ~ vc |<v|D|c>|2 (Ec-Ev-)

v

c

P = P0 = -iGG

P = P0 = -iGGExcitons?

IP-RPA calculation

(Independent Quasiparticles)

---- LDA

---- RPA GW

Absorption spectrum of Solid Argon

Im [] ~ vc |<v|D|c>|2 (Ec-Ev-)

Onida Reining Rubio RMP 74, 601 (2002)

V. Olevano (2000)

Calculation with excitonic effects

(G2 via the Bethe-Salpeter equation)

Im [] ~ | vc<v|D|c> Avc|2 (E-)

Absorption spectrum of Solid Argon

->Mixing of transitions->Modification of excitation energies

TDDFT= 0 + 0 [ v + fxc ]

BSE= 40 +40 [ v +xcG

Common ingredient

Different “electrons”

(1,3)/G(2,4)

Vxc(1)/(2)

VH(1)/(2)

+=

G. Onida, L. Reining, A. Rubio, Reviews of Modern Physics 74, 601 (2002)

Back to density functionals?

Effects of oxidation on small Silicon nanoaggregates:

16.000 steps13.5 ps

Oxygen on Si10H16

M. Gatti and G. Onida, PRB 72, 1 (2005)

Ground state equilibrium structure (Density Functional calculation)

M. Gatti and G. Onida, PRB 72, 1 (2005)

Absorption spectra:TDLDA works better for clusters (finite systems) than for infinite solids.

Redshift (in eV) of the optical gap of Si10H16 after oxidation Excited state

calculations within TDDFT

(adiabatic LDA approximation)

Silane (SiH4)

Silanone (H2SiO)

FIG. 1. Schematic representation of a Stokes shift relaxation. In position (1), the cluster is in its electronic ground state, and the atomic geometry is relaxed to its lowest energy configuration. On absorption of a photon, the nanocluster undergoes a vertical electronic excitation from (1) to (2). Once in the excited electronic state, the atomic geometry of the cluster relaxes to a lower energy configuration from (2) to (3). Finally, the excited electron and hole recombine via another vertical transition, (3) to (4). The Stokes shift is defined as EA - EE

(Degoli et al., PRB 69, 155411, 2004)

H2SiO: Stokes shift relaxation

isodensity surfaces:

HOMO LUMO

Oxydized Si(100) surface

Ground State Calculations

Optical properties of Si(100):O (0.5 ML)

A. Incze, R. De Sole, G. Onida, PRB 71, 035350 (2005)

Surface Optical Spectra of Si (100):Oas a function of O coverage

A. Incze, R. De Sole, G. Onida (2005)

Optical properties of Si (113) (3x2) ADI*

*Structure: from Stekolnikov, Furthmueller and Bechstedt, PRB 68, 205306 (2003); PRB 67, 195332 (2003).

“Bulk Anisotropy” due to the very asymmetric unit cell and the limited thickness of the slab. Very difficult to get converged spectra (K. Gaal-Nagy, G.O. et al, in preparation)

In this case, the slicing technique is essential!

NANOQUANTANETWORK

Nanoscale photon absorption and

spectroscopy with electrons

nLund

(Almbladh)

Jena(Bechstedt)

Berlino(Gross,

Scheffler)

York (Godby)

Ecole Polyt.Parigi

(Reining)

Milano(Onida)

S.Sebastian(Rubio)

Louvain(Gonze)

Roma(Del Sole)

Researchers mobility: Post-Doc, Phd, diploma thesis...

European Theoretical Spectroscopy Facility: A “knowledge center”, lasting after Nanoquanta, to make the integrated resources available

“Lasting integration” is needed!

• know-how (e.g., TDDFT theory & implementations)

• tools, computer codes

• complementarity of groups (methods, systems)

ETSF (European Theoretical Spectroscopy Facility)

will offer:

KNOWLEDGE

Collaborate,Publish

Train Develope and Distribute

Motivate

UndergraduatesPhD StudentsPost DocsOther colleagues

FormulaComputer Codes

Public awareness

•Distributed•Open

Let a larger community have access

PapersReviews Books

(European Theoretical Spectroscopy Facility)

• Ab-initio “theoretical spectroscopy”:– quantitative and predictive calculations– answers to new needs, due to new experiments

• We are living a period of strong and fascinating growth of new (density-based) theoretical tools;

• International integration of resources (Theory,

knowledge and computer codes) is needed

• NANOQUANTA is today a reality; the present challenge is to build ETSF. We are on the way.

Conclusions

• users.unimi.it/etsf

• google: just search “nanoquanta”:

• www.abinit.org

Web references:

Thank you for your attention !

Si10H16

Car-Parrinello Molecular Dynamics

simulation(G.Onida and W. Andreoni,

Chem. Phys. Lett. 243, 183 (1995)

Microcanonical@ 700°K

(Ground-state adiabatic

dynamics)

Nanotubes are transparent for light polarized in the direction

orthogonal to the tube!!Marinopoulos, Reining, Rubio, Vast, Phys. Rev. Lett. 91, 046402 (2003)

-Siemens Medical Solutions, Forcheim (Germany): Dr. Martin Petersilka, Dr. Thomas von der Haar;

-Thales Research and Technology, Orsay (France): Dr. Nguyen Van Dau, magnetic devices;

-Labein Centro Tecnologico, Bilbao (Spain): Dr. Roberto Garcia, General Manager;

-Max-Lab, Lund (Sweden), Dr. Nils Martensson;

-Materials Design s.a.r.l., Le Mans (France): Dr. Erich Wimmer, president;

-Telefonica Moviles, Madrid (Spain): Dr. Igacio Camarero, Exec. director of Technology & Operations Support;

-Acreo AB, Kista (Sweden): Dr. Jan Y. Andersson, manager of the Optical Engineering dept;

-Innovent Technologieentwicklung, Jena (Germany): Dr. Detlef Stock;

-SchottGlas, Mainz (Germany): Dr. Wolfgang Mannstadt, Dr. Dirk Sprenger.

NANOQUANTA Industrial Advisory Board*

*provisional list

The ETSF will be a large facility

It will have “code-and theory-lines”

It will have users who present projects

How will the ETSF work?

TOSCA - Tools for Optical Spectra Calculation and

Analysis

Web page: users.unimi.it/etsf

INFM

Optical properties of Ge-Te alloys

Not just “academic” interest!

Why excited states? -”Useful” response to excitations (2)

Static DFT: minimization of E

Ground state:

Trajectory: extrema of the action A

Evolution of the system (its density) due to external field: TD-DFT [A]

Runge and Gross, 1984

Back to density functionals?

Time-Dependent DFT:

Nanoquanta Consensus: