A New Spin on Photoemission Spectroscopy Page: 71 of 259

have even (+) wavefunctions with respect to the plane (or would have nodes, 0 probability
amplitude, at the detector). For p-polarized light, the matrix element then goes as (+j+1?).
This matrix element will then be maximum for initial states of even spatial symmetry with
respect to the defined plane, and will in fact be zero for initial states of odd symmetry. For
s-polarized light, the situation is reversed as the matrix element will go as (+l - I?).
If we take the photoelectron wavefunction, of, to be a plane wave, eik-x, the matrix
element from equation 2.30 can be expressed as
2 Ik-xAos - P.0)
oc (E - k) (eik x ki2. (2.32)
This illustrates that the matrix element can be dependent on the initial state wavefuntion
as well as the outgoing k-vector, which can be effected by the experiment's geometry. This
also demonstrates ARPES photon energy dependence: a change in by will change EK as
well as the magnitude of k. The overlap of the outgoing plane wave and the initial state,
(eikxkb), depends on both details of the initial state wavefunction as well as the outgoing
k-vector, thus causing modulations in the intensity with photon energy (not necessarily
monotonic).30 A great example of photon energy dependent matrix elements in the double
layer HTC cuprates is given in ref. 58. One must always remember that ARPES data may be
influenced by difficult to predict matrix elements. Sometimes, these matrix element effects
can be taken advantage of. In some cases, signal from some bands can be enhanced with
respect to others due to different matrix element dependencies on photon energy, 58,59,60,61,56
photon polarization,62,63 or polarization geometry. 54 Matrix element effects can also be used
for aiding in identifying initial state characteristics such as orbital symmetry character.64
2.7 State-of-the-art ARPES
The ARPES technique has undergone enormous growth in the past decade. Much of
the current strength and popularity of ARPES is related to its symbiotic relationship with
the field of HTC cuprates. From initial observations of d-wave gap symmetry,65 to fine

50

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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/m1/71/ocr/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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