Gasparian Vladimir, Suzuki Akira
Department of Physics, California State University, Bakersfield, CA 93311, USA.
J Phys Condens Matter. 2009 Oct 7;21(40):405302. doi: 10.1088/0953-8984/21/40/405302. Epub 2009 Sep 14.
We study the influence of evanescent modes on the scaling behavior of the renormalized localization length (RLL) in 2D disordered systems, using the δ-function potential strip model and the multichain tight-binding Anderson model. In the weak disorder regime we have evaluated the RLL for large numbers of modes M. It is shown that RLL shrinks with increasing M which indicates that the electron states will remain localized in an infinitely wide system for an arbitrarily small disorder, in agreement with existing theories. In the thermodynamic limit ([Formula: see text]) for the two models, we obtain the localization length in an infinitely large system. We show that the presence of evanescent modes enhances the RLL with respect to the value obtained when evanescent modes are absent. We also derive an exact relationship between the localization length and its corresponding average mean free path for an M-channel system for the case where propagating as well as evanescent channels are present.
我们使用δ函数势条带模型和多链紧束缚安德森模型，研究了二维无序系统中倏逝模对重整化局域长度（RLL）标度行为的影响。在弱无序 regime 中，我们评估了大量模式M下的RLL。结果表明，RLL随着M的增加而收缩，这表明对于任意小的无序，电子态将在无限宽的系统中保持局域化，这与现有理论一致。在两个模型的热力学极限（[公式：见正文]）下，我们得到了无限大系统中的局域长度。我们表明，倏逝模的存在相对于不存在倏逝模时获得的值增强了RLL。我们还推导了在存在传播通道和倏逝通道的情况下，M通道系统的局域长度与其相应平均自由程之间的精确关系。
