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Gw renormalization of the electron phonon coupling

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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.

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Gw renormalization of the electron phonon coupling

  1. 1. GW renormalization of the electron-phonon couplingelectron-phonon coupling Claudio Attaccalite Institute Neel, Grenoble (France)
  2. 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. 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. 4. Electron-phonon coupling (3-fold) LUMO Changes in electronic structure → The frozen-phonon approach: EPC ~ |slope|2 Structural deformation Stepwise deformation
  5. 5. ...an old story
  6. 6. More recently... RAMAN on graphene 1/2
  7. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 20. Acknowledgments Xavier Blase Paul Boulanger Elena Cannuccia Ivan Duchemin Carina Faber Alexander Gruneis Francesco Mauri Michele Lazzeri Angel Rubio Ludger Wirtz
  21. 21. Bands renormalization Frozen phonon approach
  22. 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. 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

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