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Determination of the time scale of photoemission from the measurement of spin polarization
by Mauro Fanciulli, J. Hugo Dil
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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/1806.05895v3 (pdf) |
| Date submitted: | 2018-10-24 02:00 |
| Submitted by: | Fanciulli, Mauro |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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 is reviewed in this manuscript. In particular, the distinction between scattering EWS and interfering EWS time delay will be introduced, providing an insight in the chronoscopy of photoemission. The method is applied to the recent experimental data for Cu(111) presented in M. Fanciulli et al., PRL 118, 067402 (2017), allowing to give better upper and lower bounds for the EWS time delays.
Author comments upon resubmission
We thank the referee for the suggestions and for appreciating our work.
We agree with the recommendation about the abstract and have changed it accordingly. This manuscript is not only a review, however, since at the time of the PRL the method was not fully developed as it currently is (e.g., the distinction between scattering EWS and interfering EWS time delays was not made). We also agree that the discussion about interference needs clarification since it is a crucial point, and therefore we have made several changes in Section 1.2, but have kept the wording, given what it is argued in the following where the referee's concerns are addressed.
It is true that the term "interference" might be misleading, because for example the word interference was not used in E. Tamura et al., PRL 59, 934 (1987), where this effect was first properly described for solid targets (as well as in some of the previous similar works on atoms). Nevertheless, in several other publications the spin polarization is said to be due to: - "interference of the wave functions of continuum states reached by the photoionization process" [U. Heinzmann, G. Schonhense, J. Kessler, PRL 42, 24 (1979)], in the case of atomic targets, e.g. the s and d shells reached by an electron from a p shell. - "consequence of a quantum mechanical interference between different photoelectron partial waves", and also "interference of these continuum waves [i.e. transitions from one initial state into two different but energetically degenerated continuum states], which is nonzero if a phase-shift difference exists between the two waves" [N. Irmer et al., PRB 45,7 (1992)]. Similar wording are found in other old references, as well as in the more recent one: - "a quantum mechanical interference of two outgoing partial waves describing the photoelectron emission" [U. Heinzmann and H. Dil, J. Phys.: Condens. Matter 24, 173001 (2012)]. The point is that the term Im[M1M2*] proportional to sin(phi2-phi1) is interpreted as an interference between M1 and M2, and we decided to keep the wording extensively present in the literature. What is more important, is that now we have better addressed the central role of spin-orbit coupling. In fact, as correctly stated by the referee, application of the dipole operator in Fermi's golden rule does not allow spin-flip. Nevertheless, spin mixing in the partial channels becomes possible when spin-orbit coupling is accounted for by relativistic equations (for explicit description see J. Kessler, Polarized electrons 2nd edition, 1985, page 32 for electron scattering and section 5.2.3 for atomic photoionization). This is now stated in the present manuscript, with more stress on the role of SO.
We are confident that we have clarified the referee's concerns and that the manuscript is now ready for publication.
With best regards, Mauro Fanciulli and Hugo Dil
List of changes
Several sentences of Section 1.2 have been modified, in order to better describe the interference process. In particular:
- the possibility of spin-flip due to spin-orbit coupling is mentioned when describing the electron scattering process
- spin-orbit coupling is highlighted as a key ingredient in order to have the spin polarization in the photoelectron beam from a spin-degenerate state