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arXiv 2401.04715cond-mat.mes-hallcond-mat.str-elhep-phquant-ph
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含结的石墨烯纳米带的有效理论

An Effective Theory for Graphene Nanoribbons with Junctions

Johann Ostmeyer, Lado Razmadze, Evan Berkowitz, Thomas Luu, Ulf-G. Meißner

AI总结:

本文为含结的混合石墨烯纳米带推导了基于紧束缚拟设的有效理论,精确预测能隙和局域化性质,并通过量子蒙特卡罗验证其在Hubbard相互作用下仍适用,同时发现新型Kilimanjaro局域化并揭示了Fuji局域化的模3条件。

摘要:

石墨烯纳米带是实现容错量子电子学的一种有前景的候选体系。在该方案中,量子比特由局域态实现,这些局域态可以出现在由两条不同宽度的扶手椅型纳米带构成的混合纳米带的结上。我们基于紧束缚拟设推导了一个用于描述混合纳米带的有效理论,并利用该理论对各种混合纳米带几何结构中的能隙和局域化性质做出精确预测。我们使用量子蒙特卡罗模拟证明,在存在Hubbard相互作用的情况下,该有效理论仍然适用。我们发现,除了结上众所周知的局域化(我们称之为“Fuji”)之外,还存在一种新型的“Kilimanjaro”局域化,它弥散在混合纳米带的一段上。我们证明,在宽度为$N$和$N+2$的扶手椅型纳米带构成的混合结构中,Fuji局域化出现在对称结附近,当且仅当$N\pmod3=1$,而边缘对齐的结从不支持强局域化。这种行为不能仅仅依靠拓扑$Z_2$不变量来解释,而迄今为止$Z_2$不变量一直被认为是这些局域化的起源。

英文摘要:

Graphene nanoribbons are a promising candidate for fault-tolerant quantum electronics. In this scenario, qubits are realised by localised states that can emerge on junctions in hybrid ribbons formed by two armchair nanoribbons of different widths. We derive an effective theory based on a tight-binding ansatz for the description of hybrid nanoribbons and use it to make accurate predictions of the energy gap and nature of the localisation in various hybrid nanoribbon geometries. We use quantum Monte Carlo simulations to demonstrate that the effective theory remains applicable in the presence of Hubbard interactions. We discover, in addition to the well known localisations on junctions, which we call `Fuji', a new type of `Kilimanjaro' localisation smeared out over a segment of the hybrid ribbon. We show that Fuji localisations in hybrids of width $N$ and $N+2$ armchair nanoribbons occur around symmetric junctions if and only if $N\pmod3=1$, while edge-aligned junctions never support strong localisation. This behaviour cannot be explained relying purely on the topological $Z_2$ invariant, which has been believed the origin of the localisations to date.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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