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Momentum spectrometer for electron-electron coincidence studies on superconductors
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View: Figures


Image of FIG. 1.
FIG. 1.

Cut through the detector and spectrometer. The photon beam (yellow) is incident under 70° to the surface normal. For clarity purposes, all parts from the sample holder are removed except the sample itself and part of the shielding, which fits right into the spectrometer end plate in order to guarantee a homogeneous electric field inside the spectrometer. Two sample trajectories of emitted electrons are sketched in blue.

Image of FIG. 2.
FIG. 2.

Merging of two single-hit events to an artificial double-hit event with known time position of the pulses. Upper left and right panel show pulses from electrons A and B recorded from two different events. Both waveforms are added to simulate an event, where two electrons hit the detector. These artificial electrons are equivalent to electrons, which were created in the same light pulse but independently by two photons. The new event (lower panel) shows a typical double pulse (black), which can be used to test the pulse analysis algorithms. The result of this algorithm Xa and Xb can be compared to the known timing information of A and B.

Image of FIG. 3.
FIG. 3.

Particle loss probability as a function of time- and position difference of an electron pair on the detector. The x- and y-axis show the time difference between two consecutive hits and the distance in position between the two hits. The z-axis shows the difference between the number of hits retrieved by the respective algorithm and the real number of hits in an event-mixed sample file. Both spectra are normalized to the sum of the hits. Therefore yellow color (z-axis = 1) indicates a complete loss of all events in this region, while purple (z-axis = 0) indicates a correct retrieval of all events. Negative values indicate that events have been found which are not real at this position and time, but might have been in a neighboring bin. Application of a standard CFD (left) and pulse fitting algorithm (right). See text.

Image of FIG. 4.
FIG. 4.

(Left) Electrons from 30 eV photon impact on a Pb(111) surface detected by the spectrometer shown in Figure 1. Horizontal axis: time of flight, vertical axis: x-position of impact on the detector. Only events for which the y-position is within ±2.5 mm to the center of the detector. (Middle) Calculation of lines of same energy and emission angle for the described spectrometer and field (7.2 V/cm). (Right) Calculated lines laid with the recorded spectrum.

Image of FIG. 5.
FIG. 5.

Fermi surface cut of Pb(111)surface at photon energies of 9 eV. The parallel momentum of electrons with kinetic energies of ±0.25 eV around E F is shown. White line represents theoretical calculations perpendicular to L at 0.85 of Γ − L consistent with an inner potential of 11.8 eV.

Image of FIG. 6.
FIG. 6.

Influence of detector dead time on momentum space distributions of electron pairs. Relative momenta in the p x , p y -plane of two electrons are compared when using the standard CFD algorithm (grey) and the pulse-fit algorithm (blue). Both spectra are corrected for solid angle effects. (Left) p z of the electrons are equal (within 0.1 a.u.). (Right) p z of the electrons differs by 0.4 ± 0.1. a.u.

Image of FIG. 7.
FIG. 7.

All channels recorded for one event where two electrons hit the detector at about the same time. Channels 1−6 are the ends of the three anode layers, Channel 7 the MCP-signal, and Channel 8 the timing signal from the light source. Whereas signals are well separated on the first four Channels, they are strongly overlapping on Channels 5, 6, and 7. The assignment of two corresponding signals is done by calculating the time sum. A and A represent the pulses of the first hit, B and B the sum of the second hit.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Momentum spectrometer for electron-electron coincidence studies on superconductors