InP/GaSb core-shell nanowires: a practical proposal for Majorana modes in a full-shell hybrid geometry with hole bands

Vezzosi et al. investigate theoretically using hole bands in core-shell InP/GaSb nanowires incapsulated in a full superconducting shell. Full shell nanowire setups have the advantage of not requiring strong Zeeman energies, rather relying on orbital effects to induce a topological phase. Nonetheless, such setups suffer from the usual issue of distinguishing topological states (MZMs) from trivial. In particular, in the case of full shell nanowires, Caroli–de Gennes–Matricon states can give zero-bias peaks (ZBPs) reminiscent of MZMs. In their paper Vezzosi et al. propose that hole bands in InP/GaAs full shell nanowires could be a better platform than the previously used InAs setups [see Vaitekėnas et al. Science 367, 6485 (2020)], which have attracted both skepticism and controversy. The proposed setup using holes in this paper has the advantage of strong spin-orbit coupling (SOC) than InAs and does not rely on strain or electric fields.

The calculation in this work is solid and a nice example of how core shell nanowires and holes could be a good strategy for achieving strong SOC and, potentially, topological superconductivity. I am minded to eventually accept for SciPost, however I have some concerns since the authors are proposing a very specific platform. In particular, a more in depth discussion of the SC is required before it is possible to really assess the validity of this proposal [see (1) below)]. Nonetheless, if the authors can provide a convincing discussion of the SC then I believe this paper should be published in SciPost and hopefully will encourage experimental efforts.



(1) The authors state “in this work we make a specific and practical proposal“, however throughout — until the final paragraph — I had the question in my of which superconductor was part of this proposal (SC of course being vital for achieving TSC). It is stated at the very end “In any case, the main conclusions of our work should not be affected by the particular SC”. I am not sure I completely agree. Could the authors comment on the following:

1.1) It is stated that metallization effects could be especially important in this setup. I agree with this and think it would be worth spelling out that metallization effects will e.g. likely effectively increase the effective R of the wavefunction and therefore reduce SOC. Similar effects have been seen in before semiconductor and topological-insulator nanowires. I do not think that metallization will negate the benefits of the proposed setup in this paper, but a more in depth discussion of its impact would be useful.
1.2) The TSC region is more than an order of magnitude larger than achieved in the standard Lutchyn-Oreg model, which is the main merit of this proposal. However, Fig. 4 gives the impression that the SC does not matter so much. It would be useful here to briefly mention why it is still beneficial to have a large SC gap (e.g. well localised MZMs etc).
1.3) Although less familiar with attempts to induce superconductivity in GaAs, I worry that many SCs (e.g. Al) will result in a considerable increase in disorder of the GaAs due to the usual mechanisms: diffusion, cross hatched patterns, and spatially dependent interfaces. In assessing the viability of this proposal, it would be very useful for the authors to discuss past literature where such proximity effects have been attempted.

(2) A further concern with the combination of metallization and full shell nanowires is the lack of control over the location of the chemical potential. Other than the larger TSC region (a few meV), it is not really clear to me how this proposal mitigates that issue. Could the authors comment on whether this platform has any benefit (or is further hindered) by the lack of control over chemical potential compared to, say, InAs full shell nanowires?



(3) Another worry is that the limited gating possible in the proposed devices will mainly affect the ends of the nanowire and so will alter the wavefunction primarily in the region at the end. In the proposed setup the conjunction of gating with the likely dependence of metallization on the exact spatial extent wavefunction, seems likely that it could result in many parameters that are rather smooth at the end of the nanowire, which would result in quasi-MBSs. Could the authors comment on if they agree and how to mitigate this? Or do they intend the experiments to be done without any gating?

(4) The extension of the wavefunction around the nanowire core is also reminiscent of topological insulator nanowire. There it was shown that there can be issues inducing superconductivity close to a half-flux quantum, depending on the presence or absence of a vortex in the superconductor and the orbital effect of the states in the TI nanowire [de Juan et al. SciPost Phys. 6, 060 (2019)]. Here it seems there will also be an orbital effect not only in the full SC shell (causing a vortex), but also in the semiconductor. The period of the orbital effects in SC/SM will be different but both related to the radius of the nanowire. I worry that the induced superconductivity might be harmed by the orbital effect of the state in the core-shell nanowire. Could the authors comment on the impact of the orbital effect on induced SC in the nanowire?

(5) Finally, could the authors comment on whether the main experimental signatures of MZMs in the devices they envisage remain those of previous studies: Namely, ZBPs and Coulomb blockade spacing or if there are new signatures possible due to the core-shell nature of the nanowire?

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