Absence of Majorana oscillations in finite-length full-shell hybrid nanowires

Abstract

Majorana bound states (MBSs) located at the ends of a hybrid superconductor-semiconductor nanowire are only true zero modes if their characteristic localization length is much smaller than the nanowire length, ${\xi }_M\ll L$. Otherwise, their wave function overlap gives rise to a finite energy splitting that shows a characteristic oscillatory pattern $\sim e^{-2L/{\xi }_M}\cos (k_{F}L)$ versus external parameters that modify the Fermi momentum $k_F$. Detecting such "Majorana oscillations", measurable through low-bias conductance, has been proposed as a strategy for Majorana detection in pristine nanowires. Here we discuss how this detection scheme does not work in full-shell hybrid nanowires, an alternative design to partial-shell nanowires in which a superconductor shell fully wraps the semiconductor core. Using microscopic models, we provide both numerical simulations for Al/InAs hybrids as well as analytical approximations in terms of general nanowire parameters. We find that Majorana oscillations with flux in full-shell nanowires are absent in a wide portion of parameter space. This absence is not a signature of non-overlapping left- and right-end MBSs, but a consequence of the Majorana oscillation period being systematically larger than the flux window of odd Little-Parks lobes where Majorana zero-energy peaks are predicted to appear. Our results demonstrate that split near-zero modes or individual zero-energy crossings should not be dismissed as trivial even if they are found not to oscillate with flux.

15 pages, 9 figures. Final version

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Cited by in corpus (7)

• Josephson effect and critical currents in trivial and topological full-shell hybrid nanowires
• Subgap transport in superconductor--semiconductor hybrid islands: Weak and strong coupling regimes
• Fluxoid valve effect in full-shell nanowire Josephson junctions
• Caroli-de Gennes-Matricon Analogs in Full-Shell Hybrid Nanowires
• Superconducting bistability in floating Al islands of hybrid Al/InAs nanowires
• Fluxoid solitons in superconducting tapered tubes and bottlenecks
• Absence of Quasi-Majorana False Positives in Full-Shell Hybrid Nanowires