Division of Energy Systems Research, Ajou University, Suwon 443-749, Korea.
J Phys Condens Matter. 2012 Apr 4;24(13):135303. doi: 10.1088/0953-8984/24/13/135303. Epub 2012 Mar 9.
We study numerically the localization properties of a two-channel quasi-one-dimensional Anderson model with uncorrelated diagonal disorder within the nearest-neighbor tight-binding approximation. We calculate and analyze the disorder-averaged transmittance and the Lyapunov exponent. We find that the localization of the entire system is enhanced by increasing the interchain hopping strength t̃. From the numerical investigation of the energy dependence of the Lyapunov exponent for many different interchain hopping strengths, we find that apart from the band center anomaly, which usually occurs in strictly one-dimensional disordered systems, additional anomalies appear at special spectral points. They are found to be associated with the interchain hopping strength and occur at E = ± t̃/2 and ± t̃. We find that the anomalies at E = ± t̃ are associated with the π-coupling occurring within one energy band and those at E = ± t̃/2 are associated with the π-coupling occurring between two different energy bands. Despite having a similar origin, these two anomalies have distinct characteristics in their dependence on the strength of disorder. We also show that for a suitable range of parameter values, effectively delocalized states are observed in finite-size systems.
我们在最近邻紧束缚近似下，数值研究了无关联对角无序的双通道准一维安德森模型的局域化性质。我们计算并分析了平均透射率和 Lyapunov 指数。我们发现，通过增加链间跃迁强度 t̃，整个系统的局域化得到增强。通过对许多不同链间跃迁强度的 Lyapunov 指数随能量变化的数值研究，我们发现除了在严格的一维无序系统中通常出现的能带中心异常外，还在特殊的谱点出现了额外的异常。这些异常与链间跃迁强度有关，出现在 E = ± t̃/2 和 ± t̃处。我们发现，E = ± t̃处的异常与同一能带内的 π 耦合有关，而 E = ± t̃/2 处的异常与两个不同能带之间的 π 耦合有关。尽管具有相似的起源，但这两个异常在对无序强度的依赖关系上具有不同的特征。我们还表明，在适当的参数范围内，有限尺寸系统中存在有效离域态。
