valence photoemission spectroscopy and the many-body problem nicholas s. sirica december 10, 2012
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Valence Photoemission Spectroscopy and the Many-Body Problem
Nicholas S. SiricaDecember 10, 2012
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The Propagator within Many-Body
Physical Interpretation: Probability Amplitude
How is a transition possible?Interactions Mix States
A few distinctions exist between the propagator of many-body and that of high energy physics
|0 ⟩→∨Ψ 0𝑁 ⟩
𝑘<𝑘𝐹
𝑐𝑘=𝑏𝑘†
𝑐𝑘†=bk
𝑘>𝑘𝐹
𝑐𝑘†=𝑎𝑘
†
𝑐𝑘=𝑎𝑘
Many-body propagator-create and annihilate excitations and holes
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Photoemission SpectroscopyPhotoemission spectroscopy-experimental analogue to single particle propagator
Basic understanding of photoemission process:
Focusing on optical excitation-relate absorption to transition rate
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For photoemission being a single photon single electron process
defines
under
Where taking
yields a transition rate from
Several simplifying assumptions can then be made
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Ultimately defines an expression for the intensity of a photoemission spectrum
Contained with in this expression is an important quantity: the single particle spectral function
Physical interpretation-Probability which gives the distribution of spectral weight
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Spectral RepresentationDoes the spectral function have anything to do with the propagator? Yes, but you have to write it in the Lehmann representation
Writing the Fourier transform
Then gives
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By definition of the single particle spectral function
In separating real from imaginary components
Taking the limit
Results in
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Dyson’s Equation In order to compare to spectra, we need an explicit expression for the propagator. Use definition of the propagator as a Green’s function
For the free-particle propagator
Including interactions via a potential V
Or by multiplying through by the free-particle propagator
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Find a solution by way of successive iterations
Particle propagating through a many-body medium
→1
𝐸−𝐸0 (𝑘 )−Σ (𝑘 ,𝐸)
Taking gives a single-particle spectral function
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QuasiparticlesInterpretation of valence photoelectron spectra nicely described in context of Fermi liquid theory
Taken to be approximate single particle states in which a strongly interacting system can be mapped onto one which is weakly interacting
FT
Zk-quasiparticle residue. A measure of the strength of interactions
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Relating
Expanding the pole about the Fermi-level
Under
Possible to define quasiparticle residue in terms of an effective mass
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Thanks So Much!