准二维无序系统的电子结构

对形如N_t×N_l型准二维无序系统，只考虑格点之间的最近邻跳跃积分，采用特殊的格点编号方案，在单电子近似下，系统的哈密顿量可表示为简明对称矩阵，借助豪斯荷尔德变换将其约化为对称三对角矩阵，再利用负本征值理论及传输矩阵等方法,对系统态密度、局域长度及电导等电子结构特性进行数值计算. 重点研究了准一维四平行链和五平行链无序系统， 将结果与一维单链、准一维双链及三链系统进行对比，发现随维度的增加，系统的能带有所展宽，能态密度分布发生很大的变化，其峰值数量呈偶数规律增加. 并且在能带中心处存在有局域长度大于系统大小的扩展态，处于这些态下的系统具有较大电导. 从单链到多链，相当于扩大了系统的关联范围，使系统出现了类似非对角长程关联的行为. 关键词： 准二维无序系统 态密度 局域长度 电导

The electronic structure of quasi-two-dimensional disordered systems

For the quasi-two-dimensional disordered systems of the form of N_t×N_l, only considering the nearest-neighbor hopping integrals and using a special method to code the sites, we write the Hamiltonians of the systems as precisely symmetric matrixes, which can be transformed into three diagonally symmetric matrixes by the Householder transformation. The densities of states, the localization lengths and the conductance of the systems are calculated numerically using the negative eigenvalue theory and the transfer matrix method. We study mainly the quasi-two-dimensional disordered systems with four and five parallel chains. By comparing the results with that of the disordered systems with one chain, two chains and three chains, we find that the energy band of the system extends slightly and the distribution of the density of states changes obviously with the increase of the effective dimensionality. Especially, for the systems with four or five chains, at the energy band center, there exist extended states whose localization lengths are larger than the size of the systems, accordingly, they have greater conductance. With the increasing of the number of the chains, the correlated ranges expand and the systems present the behaviour similar to that with off-diagonal long-range correlation.