双链梯形网络变体：Aubry-André-Harper 型准周期下的局域化、多重分形与量子动力学
Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-André-Harper kind of quasiperiodicity
AI总结：
本文研究双链梯形网络及其超薄石墨烯纳米带变体在 AAH 准周期调制下的电子态局域化、多重分形和波包量子动力学，揭示能谱中心扩展态对输运行为的影响。
摘要：
在本文中，我们利用双链梯形网络的两种变体证明，施加在竖直链上的准周期 Aubry-André-Harper（AAH）调制——模拟网络中的确定性畸变——能够在此类系统的电子能谱中引发某些奇异特征。对于最简单的梯形网络，当调制强度超过阈值时，所有本征态都变为局域态；而对于模拟超薄石墨烯纳米带的第二种变体，能谱的中心部分仍然由扩展波函数占据。在这两种网络中，当调制接近临界值时，能谱中都观察到多重分形特征。我们还通过研究波包在此类装饰晶格上的量子动力学来证实上述发现。有趣的是，在纯双链梯形网络中，均方位移（MSD）随调制强度的变化以通常方式改变；而在超薄石墨烯纳米带中，MSD 的时间行为仅在强调制强度以下保持不变。我们认为，这是由于波函数在能谱中心部分的扩展性所致。我们还计算了两种网络在不同调制强度下的其他物理量，如返回概率、时间自相关函数、逆参与比的时间依赖性和信息熵，这些结果均佐证了我们的解析发现。
英文摘要：
In this paper we demonstrate, using a couple of variants of a two-strand ladder network that, a quasiperiodic Aubry-André-Harper (AAH) modulation applied to the vertical strands, mimicking a deterministic distortion in the network, can give rise to certain exotic features in the electronic spectrum of such systems. While, for the simplest ladder network all the eigenstates become localized as the modulation strength crosses a threshold, for the second variant, modelling an ultrathin graphene nano-ribbon, the central part of the energy spectrum remains populated by extended wavefunctions. The multifractal character in the energy spectrum is observed for both these networks close to the critical values of the modulation. We substantiate our findings also by studying the quantum dynamics of a wave packet on such decorated lattices. Interestingly, while the mean square displacement (MSD) changes in the usual manner in a pure two-strand ladder network as the modulation strength varies, for the ultrathin graphene nanoribbon the temporal behaviour of the MSD remains unaltered only up to a strong modulation strength. This, we argue, is due to the extendedness of the wavefunction at the central part of the energy spectrum. Other measurements like the return probability, temporal autocorrelation function, the time dependence of the inverse participation ratio, and the information entropy are calculated for both networks with different modulation strengths and corroborate our analytical findings.
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