Talking about my : theory, applications and...
Transcript of Talking about my : theory, applications and...
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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
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=
My( )?
Developers & Users
Users
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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)
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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)
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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
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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):
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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
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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
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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)
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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.
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Hp . (1)
Hp . (2)
AM, R. Del Sole, Phys. Rev. Lett., 91, 176402 (2003).
The polarization function approach
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BSETDDFT Experiment
QP-RPA
`
Density Functional Theory (fxc):Bound excitons
Resonant
Causal
AM, R. Del Sole, Phys. Rev. Lett., 91, 176402 (2003).
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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).
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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)
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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⟩
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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).
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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
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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).
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“ SELF, a shiny pot of fun and happiness”
[C. Hogan]