1. Elena Cannuccia Institut Laue-Langevin, Grenoble (France) Electron phonon renormalization ofElectron phonon renormalization of electronic band structureelectronic band structure

2. The N particleThe N particle world:world: ionsions andand electronelectronss all togetherall together Electron phonon renormalizationElectron phonon renormalization of electronic band structureof electronic band structure 3. BornOppenheimer approximationBornOppenheimer approximation a perturbative approacha perturbative approach Electron phonon at workElectron phonon at work beyond thebeyond the BornOppenheimer approximationBornOppenheimer approximation 4. The separated worlds ofThe separated worlds of phononsphonons and electronand electronss Electrons live in the bands generated by the ionic potential Phonons are the quantized ionic vibrations on the potential generated by the electrons 5. BornOppenheimer approximationBornOppenheimer approximation a perturbative approacha perturbative approach Electron phonon at workElectron phonon at work beyond thebeyond the BornOppenheimer approximationBornOppenheimer approximation 6. Coupling electrons and phonons Coupling electrons and phonons Superconductivity Joule's heating Electron relaxation (luminescence) Polaronic transport Coherent Phonons Peierls instability Raman Spectroscopy etc...... 7. EPC on the electronic structureEPC on the electronic structure Kink in the band structure Mass Enhancement Temperature dependence of band gaps A. Marini, PRL 101,106405 (2008) 8. Energy levels renormalizationEnergy levels renormalization ThermalThermal expansionexpansion Electron-PhononElectron-Phonon interactioninteraction P.B. Allen and M. Cardona Phys. Rev. B 27 4760 (1983) >> Wherethecouplingcomesfrom? 9. BornOppenheimer approximationBornOppenheimer approximation a perturbative approacha perturbative approach Electron phonon at workElectron phonon at work beyond thebeyond the BornOppenheimer approximationBornOppenheimer approximation 10. A perturbative approach:A perturbative approach: Heine-Allen-Cardona 1/2Heine-Allen-Cardona 1/2 For a review see M. Cardona, Solid State Commun. 133, 3 (2005). H (x+u)=H (x) + V scf x u + 1 2 2 V scf x2 u2 +... Using Perturbation TheoryPerturbation Theory, we get the correction to the energy Ei=i (0) i (0) + i (0) i (0) + i (0) i (1) +... First order PT Second order PT V scf (x+u)=V scf (x) + V scf x u + 1 2 2 V scf x 2 u2 +.... 11. A perturbative approach:A perturbative approach: Heine-Allen-Cardona 2/2Heine-Allen-Cardona 2/2 Debye-Waller Fan Ei() = [ 1 2 2 V scf x2 + j (EiEj) 1 V scf x j j V scf x ] u 2 Clear dependence on the Temperature B(w) = Bose function En k ()=q n' [ gn n' k q En kEn' k+q nn' k q En kEn' k ](2B(q )+1) Thermal average Average on the electronic wavefunction FINAL FORMULA 12. Alltheprevioustheorycanbereformulatedinterm ofGreen'sfunctionincludingnonadiabaticeffects Beyond the staticBeyond the static perturbation theoryperturbation theory 13. BornOppenheimer approximationBornOppenheimer approximation a perturbative approacha perturbative approach Electron phonon coupling at workElectron phonon coupling at work beyond thebeyond the BornOppenheimer approximationBornOppenheimer approximation 14. Spectroscopy: theoretical point of view What really theoreticians calculate!! 15. Finite temperature electronicFinite temperature electronic and opticaland optical properties of zb-GaNproperties of zb-GaN H. Kawai, K. Yamashita, E. Cannuccia, A. Marini Phys. Rev. B. 89, 085202 (2014) What we can do now!!! BroadeningBroadening induced by electron-phonon scattering and temperature dependence 16. The gap ofThe gap of diamonddiamond F.Giustino,etal.PRL,105,265501(2010) E.Cannuccia,Phys.Rev.Lett.107,255501(2011) Logothedisetal.PRB46,4483(1992) Electronic Gap: 7.715 eV Renormalization: 615 meV Classicalions 17. It's time to revise previous electronic structure calculations? 18. What about dynamical effects?What about dynamical effects? 19. Dynamical effects in diamondDynamical effects in diamond Logothedis et al. PRB 46, 4483 (1992) -670 meV E. Cannuccia, Phys. Rev. Lett. 107, 255501 (2011) Signature ofSignature of the dynamicalthe dynamical effectseffects 20. Breakdown of the QP pictureBreakdown of the QP picture E. Cannuccia and A. MariniE. Cannuccia and A. Marini Europ. Phys. J. B.Europ. Phys. J. B. 8585, 320 (2012), 320 (2012) 21. ConclusionsConclusions Perturbativeapproachtotheelectronphononcoupling Finitetemperatureopticalspectra BandgaprenormalizationinducedbytheEPC Dynamicaleffectsontheelectronicproperties AcknowledgmentAcknowledgment Andrea Marini CNR Rome, Italy Hiroki Kawai Tokyo University Japano 22. Thankyoufor yourattention 23. S. Ponce, G. Antonius, P. Boulanger, E. Cannuccia, et al. Comp. Mat. Science, 83, 341, (2014) Implementation of large formula: source of infinite errors but ... 24. Carbon contributionSi contrib. Total Renorm. Temp. Dep. of gap: SiC, path integral molecular dynamics Hernndez, Herrero, Ramrez, Cardona, PRB 77 045210 2008 25. Electron-phonon coupling from a MBPT perspective nk En k (T )+i n k (T ) Electronscatterswith 1phononatatime ElectronPhononSelfEnergy TemperaturedependenceSpectralFunctions Enk nk 26. A. Eiguren and C. Ambrosch-Draxl, PRL 101 036402 (2008) Quasi-particle Band Structure Induced by the Electron-phonon interaction on a surface