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Role of vibrations in electronic structure

Role of vibrations in electronic structure. Electronic structure for T=0 Sometimes considered Effect of zero-point vibrations on lattice parameters. I ndirect impact. Zero-point motion. I ndirect impact. Zero point motion. I ndirect impact. Zero point vibrations

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Role of vibrations in electronic structure

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  1. Role of vibrationsin electronic structure

  2. Electronic structurefor T=0 • Sometimesconsidered • Effectof zero-point vibrationson latticeparameters Indirectimpact

  3. Zero-point motion Indirectimpact

  4. Zero pointmotion Indirectimpact

  5. Zero pointvibrations • Something tokeep in mindwhenconstructingandevaluatingvdWfunctionals … Indirectimpact Becarefulcomparingwithexperiment!

  6. Electronic structurefor T=0 • Sometimesconsidered • Effectof zero-point vibrationson latticeparameters • Long time ignored • Effectof zero-point vibrations on band gaps

  7. Band gaps

  8. Optical gaps

  9. Electronic structurefor T>0 • Pragmaticapproach: • Temperature-dependentlatticeparameters • Temperaturesmearingtodetermine Fermi energy • Vibrationaleffectsignored • Beyondthat: • Quasi-harmonicapproximationtolatticeexpansion • Renormalizationandmanybodyeffects in electronic bands • Impact on opticalexciations … • Impact on transport …

  10. Photoemission • Quasiparticlebands Accepted hn c v N-1 electrons

  11. Quasiparticlebands • Quasiparticleequation • Kohn-Sham equation • G0W0 • GW … Sx+Sc • iterative proceedures

  12. Quasiparticlebands • Dysonequation • carries, in principle, theinformationabout ALL kindsofinteractions • Whataboutphonons? S WhyshouldGWresultsagreewithexperiment?

  13. H@W(110) D@W(110) • Experimental evidence • Splitting ofsurface band • Evidenceforphononicorigin: isotope effect D@W(110) Spectralfunction A(w) E. Rotenberg, J. Schaefer, and S. D. Kevan, PRL 84, 2925 (2000).

  14. Experimental evidence • All aboutkinks …

  15. Experimental evidenceof MB effects • … andwaterfalls

  16. Whatabouttheory?

  17. Green functionapproachtopolarons • Solution ofcomplexDysonequation

  18. Photo-absorption • Excitonformation hn c v

  19. Phonon effects in excitonspectra • includeexciton-phonon coupling • BUT do not includeexcited-stategeometry

  20. Phonon effects in excitonspectra • Excited-stateforces • …. open perspectivestophotoluminescence

  21. Summary & outlook e • wph Sx+Sc Sph te tph • Etot ERQP + i EIQP • renormalization • excitations Ee-h • transport Ee-h te-h Fe-h • geometry

  22. Program

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