Localization of non-interacting electrons in thin layered disordered systems

TL;DR

This paper investigates electron localization in thin layered disordered systems using numerical methods, confirming the one-parameter scaling hypothesis and showing exponential growth of localization length with layer number without a transition.

Contribution

It provides numerical validation of the one-parameter scaling hypothesis for layered systems and compares results with analytical theories, extending understanding of localization in disordered thin films.

Findings

Localization length grows exponentially with layer number b

No localization-delocalization transition occurs

Results align with analytical self-consistent theory and previous numerical studies

Abstract

Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov exponent. The results support the one-parameter scaling hypothesis for disorder strengths W studied and b=1,...,6. The obtained results for the localization length are in good agreement with both the analytical results of the self-consistent theory of localization and the numerical scaling studies of the two-dimensional Anderson model. The localization length near the band center grows exponentially with b for fixed W but no localization-delocalization transition takes place.