I show how much GW corrections are important not only for the band structure but also in the calculation of the electron-phonon matrix elements. I present different examples and comparison with the experimental results.

1. GW renormalization of
the electron-phonon couplingelectron-phonon coupling
Claudio Attaccalite
Institute Neel, Grenoble (France)

2. GW band structure
Dyson equation: G = G0
+ G0
ΣG
GW approximation: Σ=iGW
G0
W0
evGW
scfQPGW
scfCOHSHEX+G0
W0
PPM
Contour
deformation

3. Electron-phonon coupling
For every single particle
Hamiltonian
(Kohn-Sham, Tight-binding, etc..)
Second order expansion
Calculsabinitiodestructures électroniques et de leur dépendance en
température avec la méthode GW
Phd Thesis, Gabriel Antonius

4. Electron-phonon coupling
(3-fold)
LUMO
Changes in electronic structure
→ The frozen-phonon approach:
EPC ~ |slope|2
Structural deformation
Stepwise deformation

5. ...an old story

6. More recently...
RAMAN on graphene 1/2

7. RAMAN in graphene 2/2
K K
'
ℏ q {
q
→ D-line dispersion
→ Double resonant RAMAN
I. Pócsik et al., J. Non­Cryst. Solids 227, 1083 (1998)
P. H. Tan et al., Phys. Rev. B 66, 245410 (2002).
J. Maultzsch et al., Phys. Rev. B 70, 155403 (2004).

8. GW correction to the EPC
Pq= 4
N k
∑k
∣D kq 
, k∣2
k , −kq ,

Impact of the electron­electron correlation on phonon dispersion: Failure of LDA and GGA DFT
functionals in graphene and graphite
Michele Lazzeri, Claudio Attaccalite, Ludger Wirtz, and Francesco Mauri
Phys. Rev. B 78, 081406(R) (2008)

9. Diagrammatic approach
Electron and phonon
renormalization
of the EPC vertex
Dirac massless fermions
+
Renormalization Group
Interplay of Coulomb and electron­phonon interactions in graphene
D. M. Basko and I. L. Aleiner
Phys. Rev. B 77, 041409(R) (2008)

10. EPC in fullerenes
LDA 73 meV
evGW 101 meV
Exp. 107 meV
DFT: J. Laflamme-Janssen, PRB 2010;
GW: C. Faber, PRB 84, 155104, 2011;
Exp: Wang, JCP 2005; Hands, PRB 2008;
(3-fold)
LUMO
ev-GW
DFT-LDA
Electron-phonon potential
Electron–phonon coupling and charge­transfer excitations in organic systems from
many­body perturbation theory
C. Faber et al., J. of Material Science, 47, 7472(2012)

11. Bismuthates, Chloronitrides and
other high-Tc superconductors
Correlation­Enhanced Electron­Phonon Coupling: Applications of GW and Screened
Hybrid Functional to Bismuthates, Chloronitrides, and Other High­Tc Superconductors
Z. P. Yin, A. Kutepov, and G. Kotliar
Phys. Rev. X 3, 021011 (2013)

12. Bismuthates, Chloronitrides and
other high-Tc superconductors
critical temperature Tc
Correlation­Enhanced Electron­Phonon Coupling: Applications of GW and Screened
Hybrid Functional to Bismuthates, Chloronitrides, and Other High­Tc Superconductors
Z. P. Yin, A. Kutepov, and G. Kotliar
Phys. Rev. X 3, 021011 (2013)

13. Diamond gap?
Effect of the Quantum Zero­Point Atomic Motion on the Optical and Electronic Properties of
Diamond and Trans­Polyacetylene
Elena Cannuccia and Andrea Marini
Phys. Rev. Lett. 107, 255501(2011)
Electron­Phonon Renormalization of the Direct Band Gap of Diamond
Feliciano Giustino, Steven G. Louie, and Marvin L. Cohen
Phys. Rev. Lett. 105, 265501 (2010)

14. GW renormalization of EPC
and diamond gap
Many­Body Effects on the Zero­Point Renormalization of the Band Structure
G. Antonius, S. Poncé, P. Boulanger, M. Côté, and X. Gonze
Phys. Rev. Lett. 112, 215501 (2014)

15. New physics appears...
EPC for the K­A phonon aquires a strong doping dependence′
Doped graphene as tunable electron­phonon coupling material
C. Attaccalite et al., Nanoletters, 10, 1172(2010)

16. Experimental confirmation
Raman signature of electron-electron correlation
in chemically doped few-layer graphene
Phys. Rev. B 83, 241401(R) (2011)
Matteo Bruna and Stefano Borini
Pressure-mediated doping in graphene
Nanoletters, 11, 3564 (2011)
J. Nicolle,D. Machon, P. Poncharal,O. Pierre-Louis
and Alfonso San-Miguel

17. Simplified approach
∂ ΣGW
∂ u
q ν
≃∂ ΣCOHSEX
∂ u
q ν
∂GW
∂ u
qν
≃
( ∂G
∂ u
q ν )W
2) Constant screening respect to
the phonon displacement
1) Static screening (COHSEX) Inspired by the
Bethe-Salpeter
equation

18. The simplified approach works!
Approximation to the GW self-energy
electron-phonon coupling gradients
C. Faber et al.
Physical Review B 91 (15), 155109(2015)

19. Conclusions
1) You can get more from your GW calculations
Just move the atoms!!!
2) The new EPC matrix elements improve:
Raman, phonons, band­gap renomalization, Tc
3) New physics can appear!
4) If calculations are too heavy ….
use our simplified approach

20. Acknowledgments
Xavier
Blase
Paul
Boulanger
Elena
Cannuccia
Ivan
Duchemin
Carina
Faber
Alexander
Gruneis
Francesco
Mauri Michele
Lazzeri
Angel
Rubio
Ludger
Wirtz

21. Bands renormalization
Frozen phonon approach

22. Recent Experimental evidences
A. Grüneis et al . Phys. Rev. B 80, 085423 (2009)
Phonon dispersions around the K point
of graphite by inelastic x­ray scattering
Experimental phonon dispersion in
bilayer graphene obtained by Raman
spectroscopy
D. L. Mafra et al. Phys. Rev. B 80, 241414(R)(2009)
〈 DK
2
〉F=166eV / ˚A
〈 DK
2
〉F=164eV / ˚A GW
inelastic x­ray
Phonons dispersion of graphene

23. q =
2
ℏq  N f 
∫BZ
d k

∑i, j
∣gki ,k q, j
 2
∣k −k  kq−f 
describe the scattering of an electron from the band I to band j due to the phonon ν
gki ,kq, j

=〈 kq, j∣ Vq∣k ,i〉
..where the electron­phonon matrix element..
Has been always considered a constant
with respect to the electron/hole doping
Electron-phonon coupling and doping