SciPost Submission Page
InP/GaSb core-shell nanowires: a novel hole-based platform with strong spin-orbit coupling for full-shell hybrid devices
by Andrea Vezzosi, Carlos Payá, Paweł Wójcik, Andrea Bertoni, Guido Goldoni, Elsa Prada, Samuel D. Escribano
Submission summary
| Authors (as registered SciPost users): | Samuel D. Escribano · Carlos Payá |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2405.07651v2 (pdf) |
| Date submitted: | 2024-10-23 13:21 |
| Submitted by: | D. Escribano, Samuel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Full-shell hybrid nanowires (NWs), structures comprising a superconductor shell that encapsulates a semiconductor (SM) core, have attracted considerable attention in the search for Majorana zero modes (MZMs). However, the predicted Rashba spin-orbit coupling (SOC) in the SM is too small to achieve substantial topological minigaps. In addition, the SM wavefunction spreads all across the section of the nanowire, leading typically to a finite background of trivial subgap states with which MZMs may coexist. To overcome both problems, we explore the advantages of utilizing core-shell hole-band NWs as the SM part of a full-shell hybrid, with an insulating core and an active SM shell. In particular, we consider InP/GaSb core-shell NWs, which allow to exploit the unique characteristics of the III-V compound SM valence bands. We demonstrate that they exhibit a robust hole SOC that emerges from the combination of the intrinsic spin-orbit interaction of the SM active shell and the confinement effects of the nanostructure, thus depending mainly on SM and geometrical parameters. In other words, the SOC is intrinsic and does not rely on neither electric fields, which are non-tunable in a full-shell hybrid geometry, nor on the strain at the interface, contrary to what happens in Ge/Si heterostructures. As a result, core-shell SM hole-band NWs are found to be a promising candidate to explore Majorana physics in full-hell hybrid devices, addressing several challenges in the field.
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
We thank you and the Referees very much for the review of our manuscript. From the Referees input, we have made some changes to the manuscript (see below) that, although do not change the results and conclusions of our work, clarify several issues and significantly improve the quality of our work. We believe these changes satisfactory address all the questions/remarks the Referees had, and thus it is suitable for publication.
Best regards,
Samuel D. Escribano on behalf of all authors
List of changes
We refer to the responses to each referee to understand the motivation behind these changes. This is a comprehensive list with all the changes made:
- We have changed the title from "InP/GaSb core-shell nanowires: a practical proposal for Majorana modes in a full-shell hybrid geometry with hole bands" to "InP/GaSb core-shell nanowires: a novel hole-based platform with strong spin-orbit coupling for full-shell hybrid devices".
- We have modified/included two new sentences in the abstract. We no longer mention Caroli-de-Gennes subgap states, and we simply say "In addition, the SM wavefunction spreads all across the section of the nanowire, leading typically to a finite background of trivial subgap states with which MZMs may coexist". In addition, we include a better explanation of the SOC origin by saying "[...] that emerges from the combination of the intrinsic spin-orbit interaction of the SM active shell and the confinement effects of the nanostructure, thus depending...".
- In Section 1, at the end of the last paragraph, we have included the sentence: "We find that the SOC in these nanostructures originates from the combination of the intrinsic properties of the SM active layer and the radial confinement."
- In Section 2, in the fourth paragraph, we now include two more sentences. One is "However, different growing and fabrication methods, and particularly the ultimate incorporation of the SC outer shell in the hybrid NW, may change the position of this Fermi level. In this respect, we note that...". And the other one, at the end, is "Note also that other strategies to engineer the band alignment of hybrid quantum devices are currently being investigated. For example, in a recent experimental work [60], argon milling is used to modify the SC-SM interface while maintaining its high quality."
- In Section 2, at the end of the last paragraph, we clarify that "We make sure that our inhomogeneous FEM grid preserves the D6 symmetry of the hexagonal cross-section, which otherwise could introduce spurious solutions."
- In Section 3.2, in the last paragraph, we clarify that "Specifically, it is due to the radial confinement imposed by the nanostructure which breaks the translation symmetry of the crystal structure of this tetravalent SM".
- In Section 3.3, the third paragraph is new.
- In Section 3.4, the last paragraph has been extended.
- The title of Section 4 is now "Discussion and conclusions" and not only "Conclusions".
- In Section 4, in the first paragraph, we now clarify that "On the one hand, the tubular shape reduces the spread of the wave function across the NW section, confining it to the region close to the SC-SM interface. According to what happens in electron-based full-shell hybrid NWs, this should dramatically reduce the number of CdGM analogs coexisting with the MZMs [17]."
- In Section 4, in the second paragraph, we now explicitly say "Instead, it depends on the degree of HH and LH hybridization, ultimately regulated by the confinement strength provided by the NW radius."
- In Section 4, in the third paragraph, we include the sentence "Nonetheless, smaller radii require larger magnetic fields to achieve the topological phase, which may be detrimental to the parent superconductor. Therefore, a trade-off R must be chosen based on the SC material."
- In Section 4, the seventh and ninth paragraphs have been extended.
- In Section 4, we have included a new paragraph at the end.
- In the Appendix B, just before Eq. (39), we now clarify that "We note that this ansatz for the radial wavefunction is only valid for a core-shell NW with a thin w compared to R."
- Footnotes 5, 6 and 7 are new.
- Typos have been corrected, as well as some style issues.
- The references have been updated.
Current status:
Reports on this Submission
Report
I am very grateful to the authors for the extensive reply as well as the revised manuscript! These have helped to clear up some of my previous confusion - I was under the impression that the interaction described by alpha was within one subband, not between subbands.
I understand now the authors' results, and I think they are interesting. My main question however is the following: The main result, a coupling between the two lowest m_F=1/2 subbands as in Eq. (1) has already been shown in Eq. (3) in Ref. [50] (Kloeffel et al., PRB 84, 195314 (2011)): the term with the $C$ prefactor is identical to what the authors find.
This thus raises a major question: The paper positions itself mainly as showing strong spin-orbit in this proposed system. A very similar result (same order of magnitude) has previously been demonstrated for Ge, a platform that already exists. Is this sufficient to claim "Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work"?
Currently, Ref. [50] is somewhat dismissed in the beginning of the paper as "However, these favorable properties stem from the strain introduced at the
Ge/Si heterostructure interface [50–52], which imposes specific design constraints." The term in Ref. [50] that corresponds to the author's results is *without* strain, however. Hence, I believe the relationship to this (and possibly other papers) is not properly discussed in this paper. This also hinders me in making an assessment where this paper should be published.
If the authors can make a compelling argument for why their proposal is fundamentally better than the previous literature, then I would suggest publication in SciPost Physics. If not, then I would propose to publish in SciPost Physics Core. In both cases, I would like to ask the authors to consider my other points listed below.
Other points with regards to this manuscript:
- I misunderstood the paper when I read it first. There is a reason for this: the authors use symbols as for the conduction band case ($\alpha$) and initially do not define what they mean with "spin-orbit" (this has only slightly improved in the revised version). In fact, Ref. [50] has the same term but does not call it spin-orbit interaction (Ref. [50] later derives a Rashba type SOI). I would suggest to the authors to (i) define what they call spin-orbit already in the beginning of Sec. 3.2, and not just in the appendix (and even with the appendix, I had to read all the previous papers to understand what was going on - it would be great to make this more self-contained), (ii) give an argument why they call this spin-orbit interaction.
- I find App. B a stronger argument for claiming that the effect is due to the Hamiltonian and not electric field than all the arguments in Sec. 3.2. Basically, Sec. 3.2 shows through numerics what does not affect the strength of the effect. App. B shows you get the effect from the Luttinger-Kohn Hamiltonian and confinement alone. To me, it would make more sense to state this fact first, and later show that the more detailed numerics only gives small corrections.
- Why do the authors consider an insulating core at all? It is clear from the results that the effect they want to show also will appear without an insulating core (as is the case in Ref. [50] for example)
Recommendation
Ask for major revision
Report
The authors have addressed all comments in my previous report satisfactorily. I think that the revised version of the manuscript now meets the acceptance criteria of SciPost Physics.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report
I feel that the authors have largely addressed my concerns. I think the paper is of interest for future studies of full shell nanowires and potential MBSs in these systems, however for the paper to be of significant value then an analysis of the superconducting properties would have strengthened it considerably (and was what the original paper promised). Without that discussion I think the current paper just about meet SciPost's requirements.
Recommendation
Publish (meets expectations and criteria for this Journal)