A New Spin on Photoemission Spectroscopy Page: 67 of 259
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N-I EF N+1 E
N-1 EF N+1 E
Figure 2.9. Example one-electron removal and addition spectra for a non-interacting (left)
and an interacting (right) system consisting of a single band crossing EF. ARPES spectra
correspond to the one-electron removal spectra and only access the occupied part, high-
lighted in red. Figure adapted from ref. 30.
This of course is mainly just the cm,i part of equation 2.19, which we can then re-write as
I(k, w) a 17M %12f (w)A(k, w)8 (w + EK - hv)
where we have also added the Fermi function, f(w) to restrict the measured intensity to the
occupied states extended to finite temperature.
For a non-interacting system, the Green's function is given by
G(k, w) = 1 .
LJ - Ek -- irk
where 'q -* 0. Equation 2.20 then gives
A(k, w) = --8 (w - Ek).
Plugging this back into equation 2.22 reaffirms the early statement about the ARPES
spectra being delta functions as in the left side of Figure 2.9. For an interacting system, the
interactions can be formally introduced as a complex electron self-energy usually written as
E (k, w) = E'(k, w) + iE"(k, w). In this case, the Green's function is
G(k, w) = I
c - Ek- E(k, o)
with the spectral function then given by
7r (w - Ek - E'(k, w))2 + (E"(k, w))2
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Jozwiak, Chris. A New Spin on Photoemission Spectroscopy, thesis or dissertation, December 1, 2008; United States. (https://digital.library.unt.edu/ark:/67531/metadc1014237/m1/67/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.