1. 1. Impact of electronic correlation on electron-phonon couplingelectron-phonon coupling ClaudioAttaccalite InstituteNeel,Grenoble(France) Belfast27/07/2015
2. 2. Electron-phonon coupling: why? Superconductivity Joule's heating Electron relaxation (luminescence) Raman Spectroscopy
3. 3. Electron-phonon coupling: definition For every single particle Hamiltonian (Kohn-Sham, Tight-binding, etc..) Second order expansion H (x+u)=H (x) + H x u + 1 2 2 H x2 u 2 +... (3-fold) LUMO Changes in electronic structureStructural deformation Stepwise deformation EPC ~ |slope|2
4. 4. Electron-phonon coupling: how? DFT is an exact theoryDFT is an exact theory for the ground statefor the ground state (atomic structure,(atomic structure, phonons, etc..)phonons, etc..) EPC matrix elementsEPC matrix elements can be obtained from thecan be obtained from the Kohn-Sham eigenstates, butKohn-Sham eigenstates, but there is no guaranteethere is no guarantee that they are goodthat they are good
5. 5. Correction to the band structure QPKS+G(, )W (, )+... Using Many-body Perturbation Theory we can correct DFT results W ()= V ee () GW is the first order correction in terms of screened interaction It works very well!!! Aryasetiawan,F.,&Gunnarsson,O.TheGWmethod. ReportsonProgressinPhysics,61(3),237.(1998).
6. 6. ...an old story
7. 7. More recently... RAMAN on graphene 1/2
8. 8. RAMAN in graphene 2/2 K K ' q { q D-line dispersion Double resonant RAMAN I.Pcsiketal.,J.NonCryst.Solids227,1083(1998) P.H.Tanetal.,Phys.Rev.B66,245410(2002). J.Maultzschetal.,Phys.Rev.B70,155403(2004).
9. 9. GW correction to the EPC Pq= 4 N k k D kq , k2 k , kq , Impactoftheelectronelectroncorrelationonphonondispersion:FailureofLDAandGGADFT functionalsingrapheneandgraphite MicheleLazzeri,ClaudioAttaccalite,LudgerWirtz,andFrancescoMauri Phys.Rev.B78,081406(R)(2008)
10. 10. RecentExperimentalevidences A.Grneisetal.Phys.Rev.B80,085423(2009) PhonondispersionsaroundtheKpoint ofgraphitebyinelasticxrayscattering Experimentalphonondispersionin bilayergrapheneobtainedbyRaman spectroscopy D.L.Mafraetal.Phys.Rev.B80,241414(R)(2009) DK 2 F=166eV / A DK 2 F=164eV / A GW inelasticxray Phonons dispersion of graphene
11. 11. EPC in fullerenes LDA 73 meV evGW 101 meV Exp. 107 meV DFT: J. Laflamme-Janssen, PRB 2010; GW: C. Faber,J.ofMat.S.,47,7472(2012) Exp: Wang, JCP 2005; Hands, PRB 2008; (3-fold) LUMO ev-GW DFT-LDA Electron-phonon potential Electronphononcouplingandchargetransferexcitationsinorganicsystemsfrom manybodyperturbationtheory C.Faberetal.,J.ofMaterialScience,47,7472(2012)
12. 12. Bismuthates, Chloronitrides and other high-Tc superconductors CorrelationEnhancedElectronPhononCoupling:ApplicationsofGWandScreened HybridFunctionaltoBismuthates,Chloronitrides,andOtherHighTcSuperconductors Z.P.Yin,A.Kutepov,andG.Kotliar Phys.Rev.X3,021011(2013)
13. 13. Bismuthates, Chloronitrides and other high-Tc superconductors critical temperature Tc CorrelationEnhancedElectronPhononCoupling:ApplicationsofGWandScreened HybridFunctionaltoBismuthates,Chloronitrides,andOtherHighTcSuperconductors Z.P.Yin,A.Kutepov,andG.Kotliar Phys.Rev.X3,021011(2013)
14. 14. Diamond gap? EffectoftheQuantumZeroPointAtomicMotionontheOpticalandElectronicPropertiesof DiamondandTransPolyacetylene ElenaCannucciaandAndreaMarini Phys.Rev.Lett.107,255501(2011) ElectronPhononRenormalizationoftheDirectBandGapofDiamond FelicianoGiustino,StevenG.Louie,andMarvinL.Cohen Phys.Rev.Lett.105,265501(2010)
15. 15. GW renormalization of EPC and diamond gap ManyBodyEffectsontheZeroPointRenormalizationoftheBandStructure G.Antonius,S.Ponc,P.Boulanger,M.Ct,andX.Gonze Phys.Rev.Lett.112,215501(2014)
16. 16. New physics appears... EPCfortheKA phononaquiresastrongdopingdependence Dopedgrapheneastunableelectronphononcouplingmaterial C.Attaccaliteetal.,Nanoletters,10,1172(2010)
17. 17. 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
18. 18. Simplified approach GW u q COHSEX u q GW u q ( G u q )W 2) Constant screening respect to the phonon displacement 1) Static screening (COHSEX) Inspired by the Bethe-Salpeter equation W ()W (0)
19. 19. 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)
20. 20. Conclusions 1)ElectronphononcouplingfromKohnSham under/overestimatetherealone 2)ManyBodyPerturbationTheory canbeusedtocorrecttheEPC 4)Newphysicscanappear! 5)Ifcalculationsaretooheavy. useoursimplifiedapproach 3)ThenewEPCmatrixelementsimprove: Raman,phonons,bandgaprenomalization,Tc
21. 21. Acknowledgments Xavier Blase Paul Boulanger Elena Cannuccia Ivan Duchemin Carina Faber Alexander Gruneis Francesco Mauri Michele Lazzeri Angel Rubio Ludger Wirtz
22. 22. Bands renormalization Frozenphononapproach
23. 23. Electron-phonon coupling (3-fold) LUMO Changes in electronic structure The frozen-phonon approach: EPC ~ |slope|2 Structural deformation Stepwise deformation
24. 24. q = 2 q N f BZ d k i, j gki ,k q, j 2 k k kqf describethescatteringofanelectronfromthebandItobandjduetothephonon gki ,kq, j = kq, j Vqk ,i ..wheretheelectronphononmatrixelement.. Hasbeenalwaysconsideredaconstant withrespecttotheelectron/holedoping Electron-phonon coupling and doping
25. 25. Diagrammatic approach Electron and phonon renormalization of the EPC vertex Dirac massless fermions + Renormalization Group InterplayofCoulombandelectronphononinteractionsingraphene D.M.BaskoandI.L.Aleiner Phys.Rev.B77,041409(R)(2008)