GW renormalization of the electron-phonon couplingelectron-phonon coupling
Claudio AttaccaliteInstitute Neel, Grenoble (France)
GW band structure Dyson equation: G = G
0+ G
0ΣG
GW approximation: Σ=iGW
G0W
0
evGW
scfQPGW
scfCOHSHEX+G0W
0
PPM
Contourdeformation
Electron-phonon coupling
For every single particleHamiltonian
(Kohn-Sham, Tight-binding, etc..)Second order expansion
Calculsabinitiodestructures électroniques et de leur dépendance en température avec la méthode GWPhd Thesis, Gabriel Antonius
Electron-phonon coupling
(3-fold)
LUMO
Changes in electronic structure
→ The frozen-phonon approach:
EPC ~ |slope|2
Structural deformation
Stepwise deformation
...an old story
More recently... RAMAN on graphene 1/2
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).
GW correction to the EPC
Pq=4N k
∑k∣D kq , k∣
2
k ,−kq ,
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 MauriPhys. Rev. B 78, 081406(R) (2008)
Diagrammatic approach
Electron and phononrenormalization
of the EPC vertex
Dirac massless fermions+
Renormalization Group
Interplay of Coulomb and electronphonon interactions in grapheneD. M. Basko and I. L. Aleiner
Phys. Rev. B 77, 041409(R) (2008)
EPC in fullerenes
LDA 73 meVevGW 101 meVExp. 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)
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. KotliarPhys. Rev. X 3, 021011 (2013)
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. KotliarPhys. Rev. X 3, 021011 (2013)
Diamond gap?
Effect of the Quantum ZeroPoint Atomic Motion on the Optical and Electronic Properties of Diamond and TransPolyacetyleneElena Cannuccia and Andrea MariniPhys. Rev. Lett. 107, 255501(2011)
ElectronPhonon Renormalization of the Direct Band Gap of DiamondFeliciano Giustino, Steven G. Louie, and Marvin L. Cohen
Phys. Rev. Lett. 105, 265501 (2010)
GW renormalization of EPCand diamond gap
ManyBody Effects on the ZeroPoint Renormalization of the Band StructureG. Antonius, S. Poncé, P. Boulanger, M. Côté, and X. Gonze
Phys. Rev. Lett. 112, 215501 (2014)
New physics appears...
EPC for the KA phonon aquires a strong doping dependence′
Doped graphene as tunable electronphonon coupling materialC. Attaccalite et al., Nanoletters, 10, 1172(2010)
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-Louisand Alfonso San-Miguel
Simplified approach
∂ΣGW
∂uq ν≃∂ ΣCOHSEX
∂uq ν
∂GW∂uqν
≃( ∂G∂uq ν )W
2) Constant screening respect to the phonon displacement
1) Static screening (COHSEX) Inspired by the Bethe-Salpeter
equation
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)
Conclusions
1) You can get more from your GW calculationsJust move the atoms!!!
2) The new EPC matrix elements improve: Raman, phonons, bandgap renomalization, T
c
3) New physics can appear!
4) If calculations are too heavy …. use our simplified approach
Acknowledgments
Xavier Blase
Paul Boulanger
Elena Cannuccia
Ivan Duchemin
CarinaFaber
AlexanderGruneis Francesco
Mauri MicheleLazzeri
AngelRubio
LudgerWirtz
Bands renormalization
Frozen phonon approach
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=166eV / A
⟨DK2⟩F=164eV / A GW
inelastic xray
Phonons dispersion of graphene
q =2
ℏq N f ∫BZ
d k
∑i , j∣gki ,k q , j
2∣k−k kq−f
describe the scattering of an electron from the band I to band j due to the phonon ν
gki ,kq , j =⟨ kq , j∣ V q∣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
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