Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil.
J Phys Condens Matter. 2011 Oct 12;23(40):405501. doi: 10.1088/0953-8984/23/40/405501. Epub 2011 Sep 21.
In this paper we address a theoretical calculation of the electronic spectra of an Si-Ge atomic chain that is arranged in a Fibonacci quasi-periodic sequence, by using a semi-empirical quantum method based on the Hückel extended model. We apply the Fibonacci substitutional sequences in the atomic building blocks A(Si) and B(Ge) through the inflation rule or a recursion relation. In our ab initio calculations we use only a single point, which is sufficient for considering all the orbitals and charge distribution across the entire system. Although the calculations presented here are more complete than the models adopted in the literature which take into account the electronic interaction only up to the second and third neighbors, an interesting property remains in their electronic spectra: the fractality (which is the main signature of this kind of system). We discuss this fractality of the spectra and we compare them with the random arrangement of the Si-Ge atomic chain, and with previous results based on the tight-binding approximation of the Schrödinger equation considering up to the nearest neighbor.
在本文中，我们使用基于 Hückel 扩展模型的半经验量子方法，解决了由 Fibonacci 准周期序列排列的 Si-Ge 原子链的电子光谱的理论计算问题。我们通过膨胀规则或递归关系将 Fibonacci 取代序列应用于原子构建基块 A（Si）和 B（Ge）中。在我们的从头计算中，我们只使用一个单点，这足以考虑整个系统的所有轨道和电荷分布。虽然这里提出的计算比文献中采用的模型更完整，这些模型仅考虑到第二和第三近邻的电子相互作用，但它们的电子光谱仍然具有有趣的特性：分形性（这是这种系统的主要特征）。我们讨论了这些光谱的分形性，并将其与 Si-Ge 原子链的随机排列以及基于考虑最近邻的 Schrödinger 方程紧束缚近似的先前结果进行了比较。
