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Does ARPES measure the initial or the final state?

Our recent work measuring the angular distributions of photoelectrons came up with a surprising result. When we compared the angular distribution patterns determined with an ellipsoidal-mirror analyzer with the structure of the initial-state Fermi surface, we found what seemed to be very little correspondence.

By using DFT to calculate BOTH the initial and final states in photoemission from the Fermi surface of fcc Co/Cu(001) we found that the FINAL STATE determined the pattern of the photoelectrons that was observed.

This has significant implications in any angle-resolved photoemission determination of Fermi surface structure: The data you may try to interpret as an initial state such as the Fermi surface, may actually better reflect the final state in the excitation. This effect is expected to be VERY important in interpreting data from high-Tc superconductors and flat-band systems such as heavy fermion materials.

Angle-Resolved Photoemission from fcc-Co

Region of BZ Sampled vs Photon Energy: 21, 31, and 45 eV


These three diagrams show the fcc-Co Fermi surface intersected with a free-electron sphere (blue) for 3 different photon energies, 21 eV (left), 31 eV, and 45 eV (right). We expect to get photoemission intensity along the loci of the intersection of these two objects. The intensity will depend on the matrix element which varies with photon polarization and the joint-density of states of these initial (orange) and final (blue) states.

Experimental Data

Photoelectron angular distributions from the Fermi Surface of 10 ML Co/Cu(001) for hv = 21, 31, and 45 eV measured with a display-type ellipsoidal mirror analyzer. The data in are scaled to match in A-1.
First-principles computed ARPES for hv=31 eV vs polarization
(for the center image above)
                   

Photoelectron angular distributions computed from the LSDA band structure for three polarization conditions: purely s (left), s+p (mid), purely p (right) with the A vector in the horizontal plane. This corresponds to a slice through the Brillouin zone as shown with the blue free electron coutour in the center above. These data correspond to an energy width of ±0.25 eV.
Initial 3d-electron FS cross-section ±0.25 eV
(for the center image above)
         

Density of states ±0.25 eV at the Fermi level. The center of each panel is along the G-X line and the edge of each panel is ±1.74 A-1 (corresponding to the G-to-X distance). Normally the FS is a line contour but with the ±0.25 eV width, it is broader. Here minority-spin bands are red and the majority-spin FS contours are blue. On the right hand side, the calculated angular distribution from above for s+p polarized light is overlaid on the FS data. It is clear that this DOES NOT resemble the shape of the 3d Fermi surface.
Empty 4p Final States in Photoemission
                   

The empty 4p final states in that lie 31 eV above the Fermi level. These contours give the location of empty Co states that coincide with the blue FS sphere that is shown above. On the left are the pz states in the middle are the pxy states and on the right the pxy states are overlaid with the computed photoemission angular distribution. This shows conclusively that the photoemission angular distribution is dominated by FINAL STATE EFFECTS.
This page was last updated on June 21, 2003