role of vibrations in electronic structure
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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 - PowerPoint PPT PresentationTRANSCRIPT
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Role of vibrationsin electronic
structure
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Electronic structure for T=0
Sometimes consideredEffect of zero-point vibrations on lattice parameters
Indirect impact
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Zero-point motion Indirect impact
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Zero point motion Indirect impact
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Zero point vibrations
Something to keep in mind when constructing and evaluating vdW functionals …
Indirect impact
Be careful comparing with experiment!
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Electronic structure for T=0
Sometimes consideredEffect of zero-point vibrations on lattice parameters
Long time ignoredEffect of zero-point vibrations on band gaps
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Band gaps
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Optical gaps
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Electronic structure for T>0
Pragmatic approach:Temperature-dependent lattice parametersTemperature smearing to determine Fermi energyVibrational effects ignored
Beyond that:Quasi-harmonic approximation to lattice expansionRenormalization and manybody effects in electronic bandsImpact on optical exciations …Impact on transport …
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PhotoemissionQuasiparticle bands
hn
v
c
N-1 electrons
Accepted
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Quasiparticle bandsQuasiparticle equation
Kohn-Sham equation
G0W0
GW … iterative proceedures
Sx +Sc
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Quasiparticle bandsDyson equation
carries, in principle, the information about ALL kinds of interactionsWhat about phonons?
SWhy should GW results agree with experiment?
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Experimental evidenceSplitting of surface bandEvidence for phononic origin: isotope effect
H@W(110) D@W(110)
E. Rotenberg, J. Schaefer, and S. D. Kevan, PRL 84, 2925 (2000).
Spe
ctra
l fun
ctio
n A
(w)
D@W(110)
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Experimental evidenceAll about kinks …
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Experimental evidence of MB effects… and waterfalls
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What about theory?
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Green function approach to polaronsSolution of complex Dyson equation
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Photo-absorptionExciton formation
hn
v
c
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Phonon effects in exciton spectra
include exciton-phonon couplingBUT do not include excited-state geometry
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Phonon effects in exciton spectraExcited-state forces
…. open perspectives to photoluminescence
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Summary & outlook
Sx +Sc
eSph
ERQP + i EI
QP
te tph
wph
renormalization
Ee-h te-h
Fe-h
Ee-h transport
Etot
excitations
geometry
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Program