Electronic Wave Functions in One-Dimensional Disordered Systems

The nature of wave functions in a one-dimensional disordered system is examined in terms of a model system in which the central portion of a cell is represented by the same potential in all cells and only the lengths of the flat arms vary randomly from cell to cell. It has been shown previously that although most wave functions are localized, states corresponding to the resonances states of the central potential have extended wave functions. Here we show that states close to these resonances also have fairly extended wave functions throughout the physical sample. Numerical calculations on a model system formed from symmetric square wells indicate that even in a highly disordered system there are wide energy ranges close to the resonances which have fairly extended wave functions. Wave functions having energies in the allowed bands of the corresponding periodic lattice are also weakly localized, but their degree of localization is raised as a whole with an increase in disorder, whereas an increase in disorder only narrows the energy range of these fairly extended states.