二维准晶体中能隙的闭合、能隙标定以及从分子态到临界态的演化
Closing of gaps and gap labeling and passage from molecular states to critical states in a 2D quasicrystal
AI总结：
本文研究了二维准周期拼砌上紧束缚模型的能谱与能隙结构，通过连续参数追踪能带从分子态到多重分形态的演化，并提出了一种有限近似体中的能隙标定方案，在无限系统极限下等价于基于代数结构的已有方案。
摘要：
准晶体中的单电子能谱和波函数一直是一个引人入胜的问题，已知的解很少，尤其是在二维和更高维度中。本文研究了二维准周期拼砌上紧束缚模型的能谱和能隙结构。通过改变一个连续参数，我们追踪了能带结构的演化，从离散的分子态或原子态，到先前研究中广为人知的多重分形态。我们提出了一种在有限近似体中标定能隙的方案。在无限系统极限下，它等价于 Kellendonk 和 Putnam 基于该准周期系统的代数结构提出的方案。
英文摘要：
The single electron spectrum and wavefunctions in quasicrystals continue to be a fascinating problem, with few known solutions, especially in two and higher dimensions. This paper investigates the energy spectra and gap structures in tight-binding models on a quasiperiodic tiling in two dimensions. By varying a continuous parameter, we follow the evolution of the band structure from the discrete molecular or atomic states, to the multifractal states well-known from previous studies. We propose a scheme for labeling gaps in finite approximants. It is equivalent in the limit of infinite systems to the one presented by Kellendonk and Putnam based on the algebraic structure of this quasiperiodic system.
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