A New Spin on Photoemission Spectroscopy Page: 96 of 259
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S1/2 = t
r6 lo. 1/2 10.+ +1t2
En3 \\ 1 (
+1.12 2 +1 2 +1+ +./
:1.+1,2 w >2+112
+ +7 1/2
Pv2 1 2
1 2- + I 1+12 vtu +1/2 - 1+1 1/2)
Figure 3.1. Diagram of optical excitation of GaAs at F with circularly polarized light.
Schematic bandstructure at F is shown on far left, labeling high symmetry points. Atomic-
like spectral notation for the three levels at F are given. Complete level diagram of each
j, mj) level, expanded into explicit Imi, ms) basis kets is on the far right. Right circularly
polarized light of by = Eg can only make transitions labeled by the solid arrows. The labels
'3' and '1' correspond to the transitions' relative strengths.
along the photon propagation direction). Illuminated by right circularly polarized light of
by = Eg - 1.5 eV, transitions are then restricted by the last selection rule to only the
two marked by the solid arrows in the figure. The relative transition rates can be worked
out by inspecting the dipole matrix elements (J(m JA - p~mj)12) in terms of the Imi,ims)
basis. As the dipole operator conserves spin, it is clear that the relative transition rate of
the mj = -3/2 - mj = -1/2 transition to the mi = -1/2 - mj = +1/2 transition is
3 to 1. It is interesting to note how the transition rates are ruled by the Clebsch-Gordon
coefficients. Because of this imbalance in transition rates, the photocurrent obtains an im-
balance of spin-up and -down electrons. To be precise, the final state polarization (along
the photon propagation direction) can be expressed as
P = = = -50%. (3.5)
N + Nt 1+3
Note that illumination by left circularly polarized light limits the transitions to the two
marked by the dashed arrows in the figure, which will then give the exact opposite spin
polarization of +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/m1/96/: accessed April 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.