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Spin polarization induced by decoherence in a tunneling one-dimensional Rashba model
by S. Varela, M. Peralta, V. Mujica, B. Berche, E. Medina
This is not the latest submitted version.
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Submission summary
| Authors (as registered SciPost users): | Bertrand Berche · Ernesto Medina · Solmar Varela |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2301.02156v2 (pdf) |
| Date submitted: | 2023-02-27 12:07 |
| Submitted by: | Berche, Bertrand |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Basic questions on the nature of spin polarization in two terminal systems and the way in which decoherence breaks Time-Reversal Symmetry (TRS) are analyzed. We exactly solve several one-dimensional models of tunneling electrons and show the interplay of spin precession and decay of the wavefunction in either a U(1) magnetic field or an effective Spin-Orbit (SO) magnetic field. Spin polarization is clearly identified as the emergence of a spin component parallel to either magnetic field. We show that Onsager's reciprocity is fulfilled when time reversal symmetry is present and no spin polarization arises, no matter the barrier parameters or the SO strength. Introducing a Buttiker's decoherence probe, that preserves unitarity of time evolution, we show that breaking of TRS results in a strong spin polarization for realistic SO, and barrier strengths. We discuss the significance of these results as a very general scenario for the onset of the Chiral-Induced Spin Selectivity effect (CISS), now possibly matching experiments in a quantitative manner.
List of changes
We thank you and the two referees for the work done concerning our submission.
We have implemented in version 2 all the modifications suggested/recommended by the two referees.
In particular:
List of changes:
1.- Include an appendix connecting section 5 with equations of sections 2-4
2.- Clarify all missing definitions (\Gamma and k in Fig. 8). Revise the document for further omissions
3.- Eliminate |t_total| defined between equations (25) and (26)
4.- Clarify that the x_0 chosen for Fig. 13 is the same as that of Fig. 12
5.- Correct Fig. 9 with the x axis (a) starting beyond x_0 and making this clear in the text
6.- Discuss in more detail how time-reversal symmetry breaking operates in the model (Figs. 10-13)
7.- Correct typo after Eq. (9) vx=dH/dx/m
8.- Do not repeat Eq. (8) (9) in Eq. (21). Write is once and refer to it after
9.- In Eq. (22) make the corresponding changes defining t and r
10.- Put the label in the colorbar of Figs. 11 and 12
The authors
Current status:
Reports on this Submission
Report #2 by Daniel Varjas (Referee 2) on 2023-3-21 (Invited Report)
Report
The manuscript, especially the Introduction and Summary, has improved significantly by the authors addressing the comments in the first report of Referee Könye. However, I find that most of my specific clarification requests in my first report were not addressed. I ask the authors to make further clarifications as requested in my previous report, as well as the points raised by the second report of Referee Könye. I will recommend publication after these minor changes.
Report #1 by Viktor Könye (Referee 1) on 2023-3-10 (Invited Report)
- Cite as: Viktor Könye, Report on arXiv:2301.02156v2, delivered 2023-03-10, doi: 10.21468/SciPost.Report.6876
Report
The manuscript improved significantly from the first submission.
Some of the problems with the original version of the manuscript were addressed. However, I still have some comments that have not been dealt with completely.
1-, About the quantitativeness of the result. As far as I understand $x_0$ and $\varepsilon$ are parameters that don't have any physically motivated values. Tuning them to reproduce the same value for the spin polarization as expected I wouldn't consider a quantitative result. For a quantitative result I would want to see what is expected and how the results compare to it. In what way do the results match with the estimates of Ref [21] or with experiments?
At the very end of the Discussion the Authors mention quantitativeness and how a more detailed study would be necessary. I think that is a more accurate stance and the statement in the abstract is too strong.
2-, Thank you for the clarification about the novelty of the results. But since the other Referee also found this unclear I think it should be more clearly stated in the manuscript as well.
3-, I am still confused about the $x_0$ dependence. This seems like an arbitrary choice to me without any physical insight. Maybe showing how results depend on $x_0$ could be beneficial. Why is $x_0$ just not fixed in the middle of the scattering region? Somehow that would feel like a straightforward choice.
4-, Figure 12 and 13 still have different parameters, at least according to the figure labels. I would suggest to put all the parameters used in every figure for full clarity and reproducibility. Or in cases where it is the same as other cases clearly mention it.
5-, It is still not clear what is the difference between Fig 11 and Fig 12 in the manuscript. Again listing all parameters would help with clarity. If I understood correctly from the response the only difference is the value of $x_0$. Which goes back to my previous question on how can one select a realistic $x_0$ value.
Author: Bertrand Berche on 2023-03-15 [id 3482]
(in reply to Report 1 by Viktor Könye on 2023-03-10)
REFEREE The manuscript improved significantly from the first submission. Some of the problems with the original version of the manuscript were addressed. However, I still have some comments that have not been dealt with completely.
1- About the quantitativeness of the result. As far as I understand $x_0$ and $\varepsilon$ are parameters that don't have any physically motivated values. Tuning them to reproduce the same value for the spin polarization as expected I wouldn't consider a quantitative result. For a quantitative result I would want to see what is expected and how the results compare to it. In what way do the results match with the estimates of Ref [21] or with experiments? At the very end of the Discussion the Authors mention quantitativeness and how a more detailed study would be necessary. I think that is a more accurate stance and the statement in the abstract is too strong.
RESPONSE The referee is correct, the parameterization of coupling parameter would depend on e.g. the magnitude of the electron-phonon or electron-electron interaction which actually talk to the thermal reservoir. We will shrink from the claim to the quantitativeness of the results in the coupling to the reservoir. This goes also for the value of $x_0$, which is part of a minimalistic coupling (a single decoherent event). We will show the dependence on this parameter under the barrier to show it has a smooth effect. Probably the best course to fit this parameter is to assess the electron-phonon scattering length to estimate how many of these events will occur under the barrier and use as many probes as are required.
The quantitativeness goes as far as the wave vectors involved in the tunneling correspond to parameters of polaron tunneling as pointed out in Ref. [21].
REFEREE 2- Thank you for the clarification about the novelty of the results. But since the other Referee also found this unclear I think it should be more clearly stated in the manuscript as well.
RESPONSE We will modify the manuscript accordingly
REFEREE 3- I am still confused about the $x_0$ dependence. This seems like an arbitrary choice to me without any physical insight. Maybe showing how results depend on $x_0$ could be beneficial. Why is $x_0$ just not fixed in the middle of the scattering region? Somehow that would feel like a straightforward choice.
RESPONSE We will add a plot of the $x_0$ dependence of the polarization. As we answered before, where the decoherence event occurs depends on how to electron transport is coupled to the reservoir via e.g. electron-phonon coupling. In the context of another probe analogous to the Buttiker probe (the D’Amato Pastawski probe), it is placed at every point along a discrete chain describing the decoherence region.
REFEREE 4- Figure 12 and 13 still have different parameters, at least according to the figure labels. I would suggest to put all the parameters used in every figure for full clarity and reproducibility. Or in cases where it is the same as other cases clearly mention it.
RESPONSE Will correct parameters used in the figure 12 and 13.
REFEREE 5- It is still not clear what is the difference between Fig 11 and Fig 12 in the manuscript. Again listing all parameters would help with clarity. If I understood correctly from the response the only difference is the value of $x_0$. Which goes back to my previous question on how can one select a realistic $x_0$ value.
RESPONSE We replied to this concern above.
Evgeny Sherman on 2023-03-06 [id 3444]
An interesting work, still, as one of the Referees, Dr. Könye, pointed out, a toy model, distant from the real physics. The authors consider only unrealistic model of spatially uniform Rashba coupling. However, in any realistic system (independent of dimensionality) it is a random function of coordinate. Direct experimental observation has been presented here:
https://www.nature.com/articles/nphys3774
Theoretical analysis shows that the effect is generic:
https://www.sciencedirect.com/science/article/abs/pii/S1386947710002213
This randomness causes dephasing of electron' spins even for straightforward motion. Taking this effect into account could possibly make the model considered by the authors realistic.
Anonymous on 2023-05-04 [id 3643]
(in reply to Evgeny Sherman on 2023-03-06 [id 3444])Indeed a periodic model is considered with no spatial inhomogeneities. This type of model can be derived from microscopic considerations e.g. tight binding, or from group theory in strictly periodic systems (See Winkler's book on SO in semiconductors). The parameters that are attempted to fit realistic values are the SO coupling the k vectors injected in a polaron type situation and the barrier height. As was mentioned by the referee's the coupling to the environment has not microscopic model associated.
Thank you for the references