Absence of Majorana oscillations in finite-length full-shell hybrid nanowires,Physical Review B

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Absence of Majorana oscillations in finite-length full-shell hybrid nanowires
Physical Review B ( IF 3.2 ) Pub Date : 2024-09-10 , DOI: 10.1103/physrevb.110.115417
Carlos Payá ₁ , Pablo San-Jose ₁ , Carlos J. Sánchez Martínez _{2,

2} , Ramón Aguado ₁ , Elsa Prada ₁

Affiliation

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,

ξ_{M} ≪ L

. Otherwise, their wave function overlap gives rise to a finite energy splitting that shows a characteristic oscillatory pattern

\sim e^{- 2 L / ξ_{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 nonoverlapping 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.

中文翻译：

有限长度全壳混合纳米线不存在马约拉纳振荡

如果位于混合超导-半导体纳米线末端的马约拉纳束缚态 (MBS) 的特征局部长度远小于纳米线长度，则它们只是真正的零模式，

ξ_{M} ≪ L

。否则，它们的波函数重叠会产生有限的能量分裂，从而显示出特征振荡模式

\sim e^{- 2 L / ξ_{M}} cos (k_{F} L)

与改变费米动量的外部参数

k_{F}

。检测这种可通过低偏置电导测量的“马约拉纳振荡”已被提议作为原始纳米线中马约拉纳检测的策略。在这里，我们讨论这种检测方案如何不适用于全壳混合纳米线，这是部分壳纳米线的替代设计，其中超导体壳完全包裹半导体核心。使用微观模型，我们提供 Al/InAs 混合材料的数值模拟以及一般纳米线参数的分析近似值。我们发现全壳纳米线中具有通量的马约拉纳振荡在参数空间的很大一部分中不存在。这种缺失并不是左端和右端 MBS 不重叠的特征，而是马约拉纳振荡周期系统地大于奇数小帕克斯波瓣的通量窗口的结果，其中预计会出现马约拉纳零能量峰值。我们的结果表明，分裂的近零模式或单独的零能量交叉不应被视为微不足道，即使发现它们不随通量振荡。

更新日期：2024-09-10

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