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Determination of the time scale of photoemission from the measurement of spin polarization
by Mauro Fanciulli, J. Hugo Dil
This is not the latest submitted version.
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Submission summary
| Authors (as registered SciPost users): | Hugo Dil · Mauro Fanciulli |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1806.05895v2 (pdf) |
| Date submitted: | 2018-09-11 02:00 |
| Submitted by: | Fanciulli, Mauro |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The Eisenbud-Wigner-Smith (EWS) time delay of photoemission depends on the phase term of the matrix element describing the transition. Because of an interference process between partial channels, the photoelectrons acquire a spin polarization which is also related to the phase term. The analytical model for estimating the time delay by measuring the spin polarization, as introduced in M. Fanciulli et al., PRL 118, 067402 (2017), will be expanded here. In particular, a distinction between scattering EWS and interfering EWS time delay will be made, providing an insight in the chronoscopy of photoemission.
Author comments upon resubmission
We thank the referee for reading the manuscript and commenting on it. However, it appears to us that the referee despite, or because of, her/his large background knowledge has misinterpreted the main message of our manuscript and the complications involved in the measurement and analysis.
The referee suggests that we could have stopped after the first part of the manuscript (up to section 3) and then apply this method to our previous results. This suggestion appears to be based on the assumption that the ratio of the matrix elements (r) can be analytically calculated. However, such an analytical approach is only possible for atomic (and maybe molecular) orbits, but not for bands and certainly not away from high symmetry points of the Brillouin zone. In section 3, which the referee regards as questionable, confusing, and unnecessary, we show how in this general case r can be measured (or estimated) and one can thus still obtain a value (or estimate) of the time delay. Here we also include any assumption that might be made and any spurious effect that might have an influence. We consider this inclusion to be important for such a manuscript which goes beyond a letter style paper, especially as indicated in the first paragraph by the referee.
The reason that we change the binding energy instead of the photon energy, is besides the points mentioned in the manuscript, mainly technical. Any SARPES set-up is by definition capable of varying the measured binding with high accuracy, but varying the photon energy is often less trivial. This is clear for laser or discharge lamp based set-ups, but also at a synchrotron the set photon energy can only be accurately determined if one measures the position of the Fermi level. Furthermore, changing the photon energy requires the change of many parameters whereas changing the binding energy requires to change just one experimental parameter, which can be detrimental for experiments where high accuracy is needed. In general, changing the photon energy introduces changes in the photon beam (energy, intensity, polarization, focus, position) as an additional error source. (These points are now included in the manuscript)
As for some other questions the referee raises: - yes it is at some points assumed that \dot{r}=0 as clearly indicated in the text. -The energy dependency of the polarization is the whole topic of the manuscript. It is due to the change in phase, or due to the time delay, depending on how one prefers to look at it (footnote 1).
As a last remark. We don’t agree with the referee that the “electrons are distinguishable (spin) [and therefore] there is no two-path interference in this particular setup.” We are here not talking about electrons that interfere as this would require the simultaneous emission of two electrons in the same energy momentum window which would cause extreme space charge effects. We are talking about the interference of different pathways similar to the single electron double slit experiment. This interference causes the measured spin polarization, which is one of the main points of this and other manuscripts. Furthermore, it has been shown before (ref 65 and 67 for example) that transition channels with different spin expectation values can interfere.
We have not made any further changes to the manuscript based on the referee report. One point that worries us more than any scientific differences of view between the referee and ourselves, which can be resolved, is that the editor required only minor corrections although the referee report was suggesting major changes. And especially that such a decision was based on only a single referee report. We understand the difficulties in setting up a new journal, and we fully support the initiative, but we expected a scientifically more professional approach.
List of changes
A paragraph concerning the technical reason for the choice of keeping a fixed photon energy in the experiment has been added in Section 3.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2018-10-12 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1806.05895v2, delivered 2018-10-12, doi: 10.21468/SciPost.Report.610
Strengths
1 - very interesting results
2 - thorough discussion of calculation procedure
3 - nice presentation of experimental geometry
Report
I understand the authors wish to keep large parts of their work and support this decision. Then, however, I recommend to change the abstract which makes the impression this was some kind of supplemental material to their PRL while the paper is more a review of the method. Changing the second part of the abstract to "... The analytical model for estimating the time delay by measuring the spin polarization is reviewed in this manuscript. In particular, ... of photoemission. The method is then applied to recent experimental data giving upper and lower bounds for the EWS time delay in ..."
But I have a more serious problem with the abstract and also the discussion of the physics in the main text: I still don't see the interference the authors are referring to. Starting from a coherent superposition of spin-up and spin-down states reflecting the initial polarization I will have different oscillator strengths for the transition to the outgoing LEED state (spin-dependent final density of states -> photon-energy dependent polarization) but though both parts of the final wavefunction will end up at the same energy they are still "separated" by their spin. Only if spin-flipping excitations would be available I would get a two-way interference (e.g. up -> up interfering with down -> up). This, however, will not happen for simple application of the dipole operator in Fermi's golden rule. Instead, I could expect to observe the signatures of the coherent excitation adding phase terms to the whole process. The same is true for Fig. 1a where any observable oscillations are signatures of coherence but not interference.
At least this is my understanding of these two terms and the authors should either add a discussion which two pathways are actually interfering or change their wording to reflect the coherence of the excitation process (if applicable). The result does not change but the origin of the effect should be properly discussed.
Requested changes
1 - consider my suggestions in the report part and change manuscript accordingly (if necessary)