二维准晶顶角模型的电子性质

THE ELECTRONIC PROPERTIES OF THE VERTEX MODEL FOR 2-DIMENSION QUASICRYSTALS

本文研究构造在Penrose晶格上的顶角模型的电子性质。对有对称心的Penrose晶格,引入一相似变换,将紧束缚哈密顿量约化成分块对角的形式,以此化简了本征能量和本征态的数值计算,并且根据这一约化确定约三分之二的能量本征态是双重简并的,而另外三分之一的态是非简并的。用Household方法和改进的Dean方法数值求解了本征能量和本征态,并用二阶矩,反参加比和波函数空间分布等方法研究了电子态的局域性质,发现三种类型的电子态(延展态、中间态和局域态)共存于二维准晶中。此外,还对能谱中的高简并态进行了研究。

This paper is devoted to the study on electronic properties of the vertex model of the Penrose lattice with five-fold rotational symmetric axis in the framework of tight-binding Hamiltonian. A similarity transformation is introduced to reduce the Hamiltonian, which helps to determine analytically the degeneracies of the eigenstates and to simplify the numerical calculation for the eigenenergies and the eigenvectors. It is found that two thirds of the states are doubly degenerate and the remains are non-degenerate. This conclusion is confirmed by group theory. The Hoursehold and improved Dean motheds are used to obtain the energy spectra and examine the localication of the electronic states. By several methods and criteria, three kinds of wavefunction behaviors are definitely found. The highly degenerate states are also investgated.