Localization length in two-dimensional disordered systems: effects of evanescent modes.

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.