(
)
Talking about my
: theory,
applications and challenges
CNR-INFM National Research Center, Modena, 23/01/2007
Ferrari 360 “Modena”
http://en.wikipedia.org/wiki/Ferrari_360
Cilindrata: 3600 Cm3, Cilindri: 8 a V
Trazione: posteriore, Motore: posteriore longitudinale
Velocita' max: 300 km/h, Potenza max: 400 CV
Andrea Marini
http://www.fisica.uniroma2.it/~marini
(
My
=
Developers & Users
Users
)?
Performance: 200 Atoms
160 Gb BS matrices
extensive parallelization
Building 1: Direction, C command line, on-fly variables
selection
Building 2: GW (plasmon pole and real axis)
5
Building 3: Bethe-Salpeter
Building 4: TDDFT, linear response ,
ALDA (reciprocal and real space)
and beyond
4
Available on
Subversion Repository
2
Building 5: Total energy, ACFDT
Project Building 6: DFT, OEP and Generalize Kohn-Sham
3
Project Building 7: BSE, Cut-Offed Hartree Potential
Project Building 8: Collinear and not collinear SPIN extension
1
Project Building 10: Surface EELS and RAS
Project Building 9: Electron Phonon interaction (Finite temperature formalism)
Surface Spectroscopy
SELF Modules
Detector
modelling
Real space
dielectric functions
Kinematics &
scattering
Standard &
advanced models
of loss function
Reflection Electron Energy
Loss Spectroscopy (REELS)
GaAs(001)-c(4x4)
Surface geometry
analysis
Real space spectral
decomposition
Reflection Anisotropy
Spectroscopy (RAS)
Computation of
reflection electron
energy loss via
integration of slab
dielectric function in
real space:
(q-dependent,
spatial dependence)
Density Functional Theory (Exc)
The Adiabatic Connection
Fluctuation Dissipation theory
Structure of layered materials: interesting case
Covalent bonds coexist with van der Waals forces
LDA underbinds the layersbut works gret near equilibrium distance
GGA (like EXX/LDA) fails
Small energy differences
deq =6.24 a.u.
h-BN
AM, P. Garcia Gonzalez, A. Rubio; PRL 96, 136204 (2006)
Density Functional Theory (Exc)
h-BN
Fluctuation-Dissipation Theorem
Adiabatic-Connection
FDT functional (ACFDT):
Exchange and correlation
must be treated at the same level
(GGA, EXX + LDA/GGA will not work)
AM, P. Garcia Gonzalez, A. Rubio; PRL 96, 136204 (2006)
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)
Optimized effective potential method
What is the effect of long
range correlation?
Niquet et al. PRB 70, 245115 (04)
Calculated
derivative
discontinuity: 3050% of the band gap
By adding it to the
EXX+RPA band gap
the we get good band
gap
M. Grüning, AM and A. Rubio JCP124, 154108 (06)
Density Functional Theory (Vxc)
Beyond LDA (GKS)
Generalized Kohn-Sham method
What is the effect of the
spatial nonlocality?
Seidl et al. PRB 53, 3764(96)
Non locality is crucial to
reduce the derivative
discontinuity
Does it exist a LOCAL
OEP potential that
yields the correct
band-gap ?
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.
The polarization function
approach
Hp . (1)
Hp . (2)
AM, R. Del Sole, Phys. Rev. Lett., 91, 176402 (2003).
Density Functional Theory (fxc):
Bound excitons
Resonant
Causal
`
AM, R. Del Sole, Phys. Rev. Lett., 91, 176402
(2003).
TDDFT
BSE
Experiment
QP-RPA
SELF and the Many-Body World
QUASIPARTICLES
Energy Levels: PRL 88, 016403
Lifetimes: PRB 66, 161104(R)
EXCITONS
Memory Effects: PRL, 91, 256402
Complex Materials: PRL 94, 087404
(2005), PRL 96, 126104 (2006), PRL 98,
036807 (2007).
The polarization function: a
two body problem
light
The BSE is not solvable in the space
of single-time Green's functions
AM, R. Del Sole
PRL, 91, 25640
(2003)
S(tatic)BSE
Static
approximation
for W(t)
The BSE: a O(NxN)
problem
S(tatic)BSE
PRB, 67, 085307 (2003)
Haydock Recursive Method
to calculate G0 
G0 ≡〈 u 0∣−H −1∣u 0 〉
a0=〈 u 0∣H∣u0 〉
b0=0
b1 =∥ H−a0  u0∥1/ 2
u1 =H−a0 / b1 u0
a1 =〈 u1∣H∣u1 〉
Gn =[−a n −b2n1 Gn1 ]−1
b2=∥ H− a1  u1 −b 1 u0∥1/ 2
u2=[ H−a1  u1− b1 u0 ]/ b 2
a1 =〈 u1∣H∣u1 〉
b3 a2
Surfaces:
Si(100) and C(100)2x1
H
Si
Si
H
Si
M.Palummo, AM, et al., in preparation
Si
Y. Borenzstein et al. PRL 2005
200000x200000
Bethe-Salpeter
Hamiltonian
(160 Gb disk
space)
C(100) Surface: M. Palummo, O. Pulci,
R. Del Sole, AM, et al., Phys. Rev. Lett.,
94, 087404 (2005).
Surface exciton with 1 eV, binding energy. The
strongest ever observed for semiconductor surfaces
The neglection of excitonic effects leads to a RAS
qualitatively and quantitatively wrong.
Crucial excitonic effects below and above the surface
gap (4 eV).
BN nanotubes:
dimensionality effects
L. Wirtz , AM, A. Rubio, PRL 96, 126104 (2006)
Strong exciton localization.
The strong exciton
localization
dictates the fast convergence of its
binding energy to the sheet value.
The absolute position of the 1st excitonic peak is
almost independent of the tube radius.
Intrigiung (but efficent) cancellation
of the excitonic and quasiparticle gap
correction.
From Si Nanowires to
porous Silicon
M. Bruno, M. Palummo, AM, R. Del Sole, S.
Ossicini Phys. Rev. Lett. 98, 036807 (2007).
Size and orientation dependent selfenergy corrections.
Huge
excitonic
dimensionality).
Clear difference between
the measured optical and
the GW QP gaps. Crucial
excitonic effects.
PS modelized using a
gaussian distribution of Si
nanowires.
effects
(reduced
“ SELF, a shiny pot of fun and happiness”
[C. Hogan]