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
INFM
• 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:
Posters!
A
initiative
Why excited states?
-Spectroscopies (experimental characterization)
C20
H. Prinzbach et al.
Nature 407, 60 (2000)
hn
e-
Why excited states?
-”Useful” response to excitations (1)
Photoluminescence in nc-Si:H films
RT PL excited with a He-Cd laser
Vs = -50
Vs = -25
Vs = 0
Vs = 25
PL Intensity (cts)
80
60
40
20
c. 2.5 eV
c. 0.6 eV
0
500
600
700
800
Wavelength (nm)
900
Why excited states?
-”Useful” response to excitations (3)
Why ab-initio?
• “first principles”:
no parameters (ingredients: N,Z)
“Just” solve Schroedinger equation!
• 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
Surface optical reflectivity - study of anisotropy spectra
Tools to analyse the
calculated spectra
Layer-by-layer
spectrum decomposition
example: Si(100)(2x1)
C.Hogan, R. Del Sole, and G.Onida, PRB 68, 035405 (2003)
ab-initio methods
“First principles” calculations = theory without free parameters
Y=Y(r1,r2,.....,rN) ?
• ground state:
– Density Functional
Theory (DFT) (1964):
Y->r
E=E[r]
(W.Kohn: Nobel prize 1998)
Spectroscopy: one
needs also the
• excited electronic
states
– C.I. (Quantum Chemistry)
– Green’s functions
(1965-->’80-->today)
1984: TDDFT! (Runge, Gross):
r = r(r,t)
A = A [r(t),t]
theory:
Which excitations?
hn
optical
reflectivity
absorption
hn
probe
hn
photoemission
inverse photoemission
electronic
STM (I/V)
ee-
hn
e-
electron energy-loss
eE,q
• Photoemission:
hn
e-
One measures EQP = EN – EN-1 = poles of G
The algebraic sum of the EQP measured in photoemission and
inverse photoemission yields the quasiparticle gap (Egap-QP)
• Absorption:
hn
hn = optical gap
Egap-opt = E’N – EN ≠ EN+1 + EN-1 – 2EN = Egap-QP
QP and optical gaps coincide only when excitonic effects are negligible
(Independent Quasiparticles approximation).
What is an absorption spectrum?
c
v
Independent quasiparticles and transitions?
c
hn
v
P = P0 = -iGG
Im [e] ~ vc |<v|D|c>|2 d (Ec-Ev-)
Absorption spectrum of Solid Argon
---- LDA
---- RPA
GW
IP-RPA calculation
(Independent
Quasiparticles)
P=
Excitons?
P0 = -iGG
Im [e] ~ vc |<v|D|c>|2 d (Ec-Ev-)
Absorption spectrum of Solid Argon
Calculation
with excitonic
effects
(G2 via the
Bethe-Salpeter
equation)
Im [e] ~ | vc<v|D|c> Avc|2 d (E-)
->Mixing of transitions
->Modification of excitation energies
V. Olevano (2000)
Onida Reining Rubio
RMP 74, 601 (2002)
Back to density functionals?
dVH(1)/dr(2)
d(1,3)/dG(2,4)
BSE
c= 4c
TDDFT
c = c0 + c0 [ v + fxc ] c
Different “electrons”
=
4c [ v +d /dG] c
+
0
0
xc
Common
ingredient
dVxc(1)/dr(2)
+
G. Onida, L. Reining, A. Rubio,
Reviews of Modern Physics 74, 601 (2002)
Effects of oxidation on small Silicon
nanoaggregates:
Oxygen on Si10H16
Ground state
equilibrium structure
(Density Functional
calculation)
16.000 steps
13.5 ps
M. Gatti and G. Onida, PRB 72, 1 (2005)
Redshift (in eV) of
the optical gap of Si10H16 after oxidation
Excited state
calculations
within TDDFT
(adiabatic LDA
approximation)
Silanone (H2SiO)
Silane (SiH4)
Absorption
spectra:
TDLDA works
better for clusters
(finite systems)
than for infinite
solids.
M. Gatti and G. Onida, PRB 72, 1 (2005)
H2SiO:
Stokes shift relaxation
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)
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):O
as 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!
York
(Godby)
Berlino
(Gross,
Scheffler)
Jena
(Bechstedt)
Lund
(Almbladh)
Ecole Polyt.
Parigi
(Reining)
n
Milano
(Onida)
Roma
(Del Sole)
S.Sebastian
(Rubio)
NANOQUANTA
NETWORK
Nanoscale photon absorption and
spectroscopy with electrons
Researchers mobility: Post-Doc, Phd, diploma thesis...
Louvain
(Gonze)
European Theoretical Spectroscopy Facility:
A “knowledge center”, lasting after
Nanoquanta, to make the integrated
resources available
“Lasting integration” is needed!
ETSF (European Theoretical Spectroscopy Facility)
will offer:
• know-how (e.g., TDDFT theory & implementations)
• tools, computer codes
• complementarity of groups (methods, systems)
•Distributed
•Open
KNOWLEDGE
(European Theoretical Spectroscopy Facility)
Train
Undergraduates
PhD Students
Post Docs
Other colleagues
Develope
and Distribute
Collaborate,
Publish
Formula
Computer Codes
Papers
Reviews
Books
Motivate
Public
awareness
Let a larger community have access
Conclusions
• 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.
Web references:
• users.unimi.it/etsf
• google: just search “nanoquanta”:
• www.abinit.org
Thank you
for your
attention !
Si10H16
(Ground-state
adiabatic dynamics)
Microcanonical
@ 700°K
Car-Parrinello
Molecular Dynamics
simulation
(G.Onida and W. Andreoni,
Chem. Phys. Lett. 243,
183 (1995)
Nanotubes are transparent
for light polarized in the direction
orthogonal to the tube!!
NANOQUANTA Industrial Advisory Board*
-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.
*provisional list
How will the ETSF work?
The ETSF will be a large facility
It will have “code-and theory-lines”
It will have users who present projects
TOSCA - Tools for Optical
Spectra Calculation and
Analysis
Web page: users.unimi.it/etsf
INFM
Why excited states?
-”Useful” response to excitations (2)
Optical properties
of Ge-Te alloys
Not just “academic” interest!
Back to density functionals?
Static DFT: minimization of E
Ground state:

Time-Dependent DFT:
Trajectory: extrema of the action A
Evolution of the system (its density) due to
external field: TD-DFT [A]
Runge and Gross, 1984
Nanoquanta Consensus: