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
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
Photoemission SpectroscopyPhotoemission spectroscopy-experimental analogue to single particle propagator
Basic understanding of photoemission process:
Focusing on optical excitation-relate absorption to transition rate
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
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
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
By definition of the single particle spectral function
In separating real from imaginary components
Taking the limit
Results in
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
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
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
Relating
Expanding the pole about the Fermi-level
Under
Possible to define quasiparticle residue in terms of an effective mass
Thanks So Much!
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