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Number conserving theory for topologically protected degeneracy in one-dimensional fermions

机译：一维费米子拓扑受保变性的数守恒理论

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摘要

Semiconducting nanowires in proximity to superconductors are among promising candidates to search for Majorana fermions and topologically protected degeneracies, which may ultimately be used as building blocks for topological quantum computers. The prediction of neutral Majorana fermions in the proximity-induced superconducting systems ignores number conservation and thus leaves open the conceptual question of how a topological degeneracy that is robust to all local perturbations arises in a number-conserving system. In this work, we study how local attractive interactions generate a topological ground-state near-degeneracy in a quasi-one-dimensional superfluid using bosonization of the fermions. The local attractive interactions opens a topological quasiparticle gap in the odd channel wires (with more than one channel) with end Majorana modes associated with a topological near-degeneracy. We explicitly study the robustness of the topological degeneracy to local perturbations and find that such local perturbations result in quantum phase slips, which split of the topological degeneracy by an amount that does not decrease exponentially with the length of the wire, but still decreases rapidly if the number of channels is large. Therefore a bulk superconductor with a large number of channels is crucial for true topological degeneracy.
机译：超导体附近的半导体纳米线是寻找马里亚纳费米子和受拓扑保护的简并性的有前途的候选者，它们最终可被用作拓扑量子计算机的构建基块。在邻近感应超导系统中对中性马约拉那费米子的预测忽略了数守恒，因此留下了一个概念问题，即在数守恒系统中如何产生对所有局部扰动都健壮的拓扑简并性。在这项工作中，我们研究如何利用费米子的玻化作用在准一维超流体中产生局部吸引相互作用，从而产生拓扑基态近简并。局部吸引相互作用在奇数通道线（具有多个通道）中打开了拓扑准粒子间隙，末端马约拉那模式与拓扑近简并相关。我们明确研究了拓扑退化对局部扰动的鲁棒性，并发现这种局部扰动会导致量子相位滑移，量子滑移将量子退化退化的量不会随导线的长度呈指数下降，但如果减小则仍会迅速减小通道数很大。因此，具有大量通道的体超导体对于真正的拓扑退化至关重要。

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