Parafermionic zero modes are a novel set of excitations displaying non-Abelian statistics somewhat richer than that of Majorana modes. These modes are predicted to occur when nearby fractional quantum Hall edge states are gapped by an interposed superconductor. Despite substantial experimental progress, we argue that the necessary crossed Andreev reflection in this arrangement is a challenging milestone to reach. We propose a superconducting quantum dot array structure on a fractional quantum Hall edge that can lead to parafermionic zero modes from coherent superconducting forward scattering on a quantum Hall edge. Such coherent forward scattering has already been demonstrated in recent experiments. We show that for a spin-singlet superconductor interacting with loops of spin unpolarized $2/3$ fractional quantum edge, even an array size of order 10 should allow one to systematically tune into a parafermionic degeneracy.

中文翻译：

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Z / 3分数量子霍尔态不带Andreev后向散射的Z3泛铁离子零模式

超铁离子零模式是一组新颖的激发，显示出比阿马里亚纳模式更丰富的非阿贝尔统计量。当附近的分数量子霍尔边缘状态被插入的超导体形成间隙时，预计会发生这些模式。尽管取得了重大的实验进展，但我们认为，在这种安排中必要的穿越Andreev的反思是一个具有挑战性的里程碑。我们在分数量子霍尔边缘上提出了一种超导量子点阵列结构，该结构可导致量子霍尔边缘上的相干超导正向散射导致超仿生零模。在最近的实验中已经证明了这种相干前向散射。我们表明，对于自旋单超导体与非极化自旋环相互作用$\mathrm{2个}/3$ 分数量子边缘，即使阵列大小约为10阶，也应允许其系统地调谐到超铁离子简并中。