SciPost Submission Page
Model for missing Shapiro steps due to bias-dependent resistance
by S. R. Mudi, S. M. Frolov
Submission summary
| Authors (as registered SciPost users): | Sergey M. Frolov · Sanchayeta Mudi |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2106.00495v3 (pdf) |
| Date submitted: | Sept. 26, 2025, 5 p.m. |
| Submitted by: | Sergey M. Frolov |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
Majorana zero modes are predicted in several solid state systems such as hybrid superconductor-semiconductor structures and topological insulators coupled to superconductors. One of the expected signatures of Majorana modes is the fractional 4$\pi$ Josephson effect. Evidence in favor of this effect often comes from a.c. Josephson effect measurements and focuses on the observation of missing first or higher odd-numbered Shapiro steps. However, the disappearance of the odd Shapiro steps has also been reported in conventional Josephson junctions where no Majorana modes are expected. In this paper, we present a phenomenological model that displays suppression of the odd Shapiro steps. We perform resistively-shunted junction model calculations and introduce peaks in differential resistance as function of the bias current. In the presence of only the standard 2$\pi$ Josephson current, for chosen values of peak positions and amplitudes, we can suppress the odd Shapiro steps, or any steps, thus providing a possible explanation for the observation of missing Shapiro steps.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Dear Editors,
We are coming back to this paper which has now proven to be an important result in identifying false positive signatures of topological phenomena in condensed matter physics. The paper has been cited 9 times according to Google Scholar. It led the original authors that found a pattern of missing Shapiro steps to perform follow-up experiments and analysis and reconsider their exotic explanation in terms of topological superconductivity. It has become part of an analytical review article that is going to be published in Science. We hope the paper is now proven to be suitable for Scipost Physics.
We are coming back to this paper which has now proven to be an important result in identifying false positive signatures of topological phenomena in condensed matter physics. The paper has been cited 9 times according to Google Scholar. It led the original authors that found a pattern of missing Shapiro steps to perform follow-up experiments and analysis and reconsider their exotic explanation in terms of topological superconductivity. It has become part of an analytical review article that is going to be published in Science. We hope the paper is now proven to be suitable for Scipost Physics.
List of changes
We explained the meaning of "Resonance" and made other clarifications throughout the text based on the report of the referee.
Current status:
In refereeing
Reports on this Submission
Report
Dear Editor,
The authors of the manuscript titled "Model for missing Shapiro steps due to bias-dependent
resistance" presents " have clarified their manuscript in response to the comments by the referee.
The clarifications have made the point of the manuscript evident.
The revisions have revealed three presentation issues that are simple to remedy and are listed below:
(1) The resistance profile obtained in Fig. 2a is a rather "fine-tuned" explanation particularly
in the case of a large number of missing Shapiro steps. For example, if the frequency of the RF
radiation f is changed by about 10%, the steps would move out of sync from the phases restoring the
Shaprio steps. The authors should discuss the extent of this fine-tuning as well as proposed ways
to test phenomenological model (Eq. 1) proposed here. The key point is that the profile R(I) should
not depend on the frequency and power of the RF radiation. It would be good for the conclusion
of the manuscript to discuss the fine-tuning issue and possible routes to test the presented
explanation.
(2) On page 5 the authors state "For example, at f = 1 GHz, the voltage of the first Shapiro....
. To identify resistance peaks occurring at a
µV voltage of a few microVolts, the experiments must have
a voltage resolution smaller than that. This is not the
case for most relevant experiments".
This is a bit confusing because the Shapiro step occurs at
a dc current which is a voltage step in Fig 2c should be of the same order as that of the resonance.
This technically appears to not be the case in the first line of Table 1.
It would be good for the authors to elaborate on either why these energy scales are different or
if not then on the prospects of measuring both R(I) and Shapiro steps on the same device in
future experiments. This provides an opportunity to elaborate on the key value of this explanation
is that it is testable, in principle, by measuring (dV/dI)(I) or (dI/dV)(V).
(3) On page 2 the authors state "The modification
is that we allow for a bias-dependent resistance
R(I), a function of our choice, to mimic the resonances
above the switching current often seen in the experimental
data." At this point it is not clear how this would be measured. It would
be great if the authors can elaborate on this along the lines of
"Therefore, to estimate the frequency corresponding
to resistance peaks, we first extract the current
bias at which these resistance peaks occur. The ‘resonance
voltage’ is the measured voltage at these resistance
peaks." as the authors explain on page 4.
In summary, I think that with the revisions and provided the above
clarifications are made, the manuscript provides a testable and interesting
phenomenological model of non-topological Shapriro steps. This can
provide direction to testing for false positive cases of identifying topological
states via Shapiro steps.
The authors of the manuscript titled "Model for missing Shapiro steps due to bias-dependent
resistance" presents " have clarified their manuscript in response to the comments by the referee.
The clarifications have made the point of the manuscript evident.
The revisions have revealed three presentation issues that are simple to remedy and are listed below:
(1) The resistance profile obtained in Fig. 2a is a rather "fine-tuned" explanation particularly
in the case of a large number of missing Shapiro steps. For example, if the frequency of the RF
radiation f is changed by about 10%, the steps would move out of sync from the phases restoring the
Shaprio steps. The authors should discuss the extent of this fine-tuning as well as proposed ways
to test phenomenological model (Eq. 1) proposed here. The key point is that the profile R(I) should
not depend on the frequency and power of the RF radiation. It would be good for the conclusion
of the manuscript to discuss the fine-tuning issue and possible routes to test the presented
explanation.
(2) On page 5 the authors state "For example, at f = 1 GHz, the voltage of the first Shapiro....
. To identify resistance peaks occurring at a
µV voltage of a few microVolts, the experiments must have
a voltage resolution smaller than that. This is not the
case for most relevant experiments".
This is a bit confusing because the Shapiro step occurs at
a dc current which is a voltage step in Fig 2c should be of the same order as that of the resonance.
This technically appears to not be the case in the first line of Table 1.
It would be good for the authors to elaborate on either why these energy scales are different or
if not then on the prospects of measuring both R(I) and Shapiro steps on the same device in
future experiments. This provides an opportunity to elaborate on the key value of this explanation
is that it is testable, in principle, by measuring (dV/dI)(I) or (dI/dV)(V).
(3) On page 2 the authors state "The modification
is that we allow for a bias-dependent resistance
R(I), a function of our choice, to mimic the resonances
above the switching current often seen in the experimental
data." At this point it is not clear how this would be measured. It would
be great if the authors can elaborate on this along the lines of
"Therefore, to estimate the frequency corresponding
to resistance peaks, we first extract the current
bias at which these resistance peaks occur. The ‘resonance
voltage’ is the measured voltage at these resistance
peaks." as the authors explain on page 4.
In summary, I think that with the revisions and provided the above
clarifications are made, the manuscript provides a testable and interesting
phenomenological model of non-topological Shapriro steps. This can
provide direction to testing for false positive cases of identifying topological
states via Shapiro steps.
Recommendation
Publish (meets expectations and criteria for this Journal)