Valence Photoemission Spectroscopy and the Many-Body Problem - PowerPoint Presentation

Slide1

Valence Photoemission Spectroscopy and the Many-Body Problem

Nicholas S.

Sirica

December 10, 2012Slide2

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 holesSlide3

Photoemission Spectroscopy

Photoemission spectroscopy-experimental analogue to single particle propagator

Basic understanding of

p

hotoemission process:

Focusing on optical excitation-relate absorption to transition rateSlide4

For photoemission being a single photon single electron process

defines

under

Where taking

yields a transition rate from

Several simplifying assumptions can then be madeSlide5

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 Slide6

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 Slide7

B

y definition of the single particle spectral function

In separating real from imaginary components

Taking the limit

Results in Slide8

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 Slide9

Find a solution by way of successive iterations

Particle propagating through a many-body medium

Taking

gives a single-particle spectral function

 Slide10

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

Z

k

-quasiparticle residue. A measure of the strength of interactionsSlide11

Relating

Expanding the pole about the Fermi-level

Under

Possible to define

quasiparticle

residue in terms of an effective massSlide12
Slide13

Thanks So Much!