等谱但物理上不同：模对称性及其对碳纳米管的影响
Isospectral But Physically Distinct: Modular Symmetries and their Implications for Carbon Nanotori
摘要：
最近，人们对碳纳米管的性质产生了相当大的兴趣。这样的纳米环面可以根据它们的半径、它们的手性以及在连接它们所源自的纳米管的相对端时发生的扭曲来参数化。然而，在本文中，我们证明了许多物理上不同的纳米管与不同的参数，但共享相同的能带结构，能谱和电导率。这是由于被称为模块对称性的某些几何对称性而发生的，模块对称性是致密化石墨烯片的性质的直接结果。使用这些对称性，我们表明，有一个显着减少的数量与物理上不同的碳nanotori光谱不同的碳nanotori。这些模块对称性的存在也使我们能够证明，在文献中的许多陈述有关的电子性质的nanotori是不完整的，因为他们没有尊重光谱等价性，从这些对称性。我们还发现，作为这些模块对称性的结果，光谱上不同的nanotori是金属的部分是大约三倍以上，天真地预期在文献中的标准结果的基础上。最后，我们证明，这些模块化的对称性也延伸到我们的碳纳米管封装非零磁通量的情况下。
英文摘要：
Recently there has been considerable interest in the properties of carbon nanotori. Such nanotori can be parametrized according to their radii, their chiralities, and the twists that occur upon joining opposite ends of the nanotubes from which they are derived. In this paper, however, we demonstrate that many physically distinct nanotori with wildly different parameters nevertheless share identical band structures, energy spectra, and electrical conductivities. This occurs as a result of certain geometric symmetries known as modular symmetries which are direct consequences of the properties of the compactified graphene sheet. Using these symmetries, we show that there is a dramatic reduction in the number of spectrally distinct carbon nanotori compared with the number of physically distinct carbon nanotori. The existence of these modular symmetries also allows us to demonstrate that many statements in the literature concerning the electronic properties of nanotori are incomplete because they fail to respect the spectral equivalences that follow from these symmetries. We also find that as a result of these modular symmetries, the fraction of spectrally distinct nanotori which are metallic is approximately three times greater than would naively be expected on the basis of standard results in the literature. Finally, we demonstrate that these modular symmetries also extend to cases in which our carbon nanotori enclose non-zero magnetic fluxes.
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