Valence Photoemission Spectroscopy and the Many-Body Problem

1. Valence Photoemission Spectroscopy and the Many-Body Problem Nicholas S. Sirica December 10, 2012

2. 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 Many-body propagator-create and annihilate excitations and holes

3. Photoemission Spectroscopy Photoemission spectroscopy-experimental analogue to single particle propagator Basic understanding of photoemission process: Focusing on optical excitation-relate absorption to transition rate

4. 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

5. 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

6. Spectral Representation Does 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

7. By definition of the single particle spectral function In separating real from imaginary components Taking the limit Results in

8. 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

9. Find a solution by way of successive iterations Particle propagating through a many-body medium Taking gives a single-particle spectral function

10. Quasiparticles Interpretation 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

11. Relating Expanding the pole about the Fermi-level Under Possible to define quasiparticle residue in terms of an effective mass

13. Thanks So Much!