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Andreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling
by Kadin Thompson, Joachim Brand, Ulrich Zuelicke
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Submission summary
| Authors (as registered SciPost users): | Joachim Brand · Kadin Thompson · Ulrich Zuelicke |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2209.08766v2 (pdf) |
| Date accepted: | 2023-03-27 |
| Date submitted: | 2023-01-27 04:25 |
| Submitted by: | Zuelicke, Ulrich |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
A topological superfluid phase characterized by an emergent chiral-p-wave pair potential is expected to form in a two-dimensional Fermi superfluid subject to s-wave pairing, spin-orbit coupling and a large-enough Zeeman splitting. Andreev bound states appear at phase boundaries, including Majorana zero modes whose existence is assured by the bulk-boundary correspondence principle. Here we study the physical properties of these subgap-energy bound states at step-like interfaces using the spin-resolved Bogoliubov-deGennes mean-field formalism and assuming small spin-orbit coupling. Extending a recently developed spin-projection technique based on Feshbach partitioning [SciPost Phys. 5, 016 (2018)] combined with the Andreev approximation allows us to obtain remarkably simple analytical expressions for the bound-state energies as well as the majority and minority spin components of their wave functions. Besides the vacuum boundary, where a majority-spin Majorana excitation is encountered, we also consider the boundary between the topological and a nontopological superfluid phase that can appear in a coexistence scenario due to the first-order topological phase transition predicted for this system. At this superfluid-superfluid interface, we find a localized chiral Majorana mode hosted by the minority-spin sector. Our theory further predicts majority-spin subgap-energy bound states similar to those found at a Josephson junction between same-chirality p-wave superfluids. Their presence affects the Majorana mode due to a coupling of minority and majority spin sectors only in the small energy range where their spectra overlap. Our results may inform experimental efforts aimed at realizing and characterizing unconventional Majorana quasiparticles.
Author comments upon resubmission
We thank both referees for their constructive reviews of our manuscript; implementing the useful suggestions made in the reports has definitely improved our manuscript. Below we elaborate in detail on the specific changes that have been made in response to the referees’ reports.
Response to Report 1 and associated changes:
We are grateful to the referee for their thoughtful report and positive evaluation of our work. In reply, we now quote each of the specific suggestions from the report and describe their implementation in the revised manuscript.
- “Modify abstract to include concrete results, e.g., the conditions for the existence of a robust Majorana mode.”
This suggestion chimes with a similar recommendation made by the other referee. For the revised version of our manuscript, we have completely rewritten the abstract to deliver a clearer and more complete overview of our methods and results.
- “What is the effect of temperature on the results? In particular, how robust are the edge states to thermal fluctuations? This is pertinent to cold-atom experiments where it is often challenging to access low temperatures, especially when applying lasers to simulate spin-orbit coupling.”
We have added the part ‘(i) Finite-temperature (T > 0) effects … significant adjustments.’ towards the end of the Conclusion section to discuss this important point.
- “Are the results sensitive to any underlying trapping potential, e.g., a harmonic trap?”
This question is addressed by the newly added sentences ‘(ii) Effect of a trapping potential … pair potential are used.’ in the last paragraph of the Conclusions section, which also contain citations to new Refs. [75-78].
- “It was not clear to me how these states might be probed in practice. The authors refer to a proposal in Ref [69] which is based on a tunnelling measurement, but it would be good (to) see some more details of how this might be adapted to the cold-atom case.”
We have expanded the discussion of experimental probes, which now fills an entire paragraph in the Conclusions section (‘Tunneling spectroscopy … vacuum boundary.’) and includes citations to new Refs. [73] and [74].
- “I would be curious to know how the results might generalize to other types of interactions, e.g., dipolar interactions. Could this be used to further enhance p-wave superfluidity?
We thank the referee for this interesting question. A preliminary answer is given in the part ‘(iii) Dipolar interactions … such systems.’ at the end of the Conclusion section, where we also express the sentiment that further research in this area would be desirable. New Refs. [79-84] are cited in this context.
Response to Report 2 and associated changes:
We thank the referee for being fully supportive of our work. Quoting from the report:
“I have only one concern that the abstract is unclear in delivering the message. The authors may provide an introduction to the theoretical formalism and the implications of the subgap states. I would like to recommend its publication after improving the abstract.”
To address the referee’s concern, we have completely rewritten the abstract so that it now contains the type of detailed information requested in the above quote from the report.
Additional changes made in the resubmitted manuscript:
In addition to changes made in response to the referee reports, we have made minor revisions to describe more precisely the connections between results presented in our manuscript and earlier work on Andreev bound states in unconventional superconductors. In particular,
(a) we reformulated footnote 1, adding the part ‘is implicit in … s-wave superfluids’ and citing new Refs. [47] and [48],
(b) revised the sentence below Eq. (50), adding the part ‘the surface bound … [48,62], including’ with citations to new Refs. [48] and [62], and
(c) revised the paragraph below Eq. (74), adding the part ‘, and it is also a special case of characteristic equations derived for bound states at general unconventional-superconductor junctions’ [47,48]’.
List of changes
This is included as part of the author comments; see above.
Published as SciPost Phys. 14, 115 (2023)