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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 Submission thread is now published as
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/2301.02156v3 (pdf) |
| Date accepted: | 2023-05-16 |
| Date submitted: | 2023-04-04 08:52 |
| Submitted by: | Berche, Bertrand |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| 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
First, we want to remind the editor/referees that for clarity, we have a pdf version of our paper with first corrections (of the first submission) highlighted in blue color and further corrections (for v2) in magenta color. This version is available upon request at bertrand.berche@univ-lorraine.fr
The first referee; Dr Konye, is correct concerning the parameterization of coupling parameter which would depend on e.g. the magnitude of the electron-phonon or electron-electron interaction which actually talk to the thermal reservoir. We shrink from the claim to the quantitativeness of the results in the coupling to the reservoir. This goes also for the value of x0, which is part of a minimalistic coupling (a single decoherent event). We now 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 corresponding to the parameters of polaron tunneling as pointed out in Ref. [21].
We have modified the manuscript concerning the novelty of the results.
We have added a plot of the x0 dependence of the polarization. As we answered before, where the decoherence event occurs depends on how 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.
The parameters used in the figure 12 and 13 are now corrected.
Concerning the queries of referee 2, Dr. Varjas, we have indicated in the introduction that the first and second neighbors refer to a tight-binding model and we have specified what the 40% polarization refers to.
The specifications that the dispersion relation refers to the Hamiltonian inside the barrier, and the change ``input’’ to ``incoming’' wave function have been done.
The velocity operator was already corrected previously.
The parameters of Fig 4 were specified (in the caption) to be the same as in Fig 3.
We have moved the introduction of the spinor definition after eqn (1), as requested by referee 2.
Color scales in Figs 11 and 12 were not modified. We believe that in a continuos color scheme, you cannot
see very well the sensitive dependence on the parameters since the eye is not so able to distinguish color changes.
The concept of level curves is well known and cannot in our opinion be misinterpreted as quantized.
Eventually, we have added the references given in the comment by Sherman.
Published as SciPost Phys. Core 6, 044 (2023)
Reports on this Submission
Report 1 by Daniel Varjas on 2023-5-4 (Invited Report)
Report
The authors have sufficiently addressed my previous comments, I recommend publication of the manuscript.