Delocalization transition in random electrified chains with arbitrary potentials

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Abstract
This paper presents a study of the transmission properties of noninteracting electrons in the presence of different types of disordered potentials along a line, in a constant electric field F. We start by considering the case of random rectangular potentials. We use the transfer-matrix method to calculate numerically the transmission coefficient as a function of energy E, field F, length L of the sample, and the amount and type of disorder. An asymptotic analytic approach, based on different physical approximations, is shown to lead to good qualitative explanations of the numerical results. Armed with the analytic understanding of the numerical results as applied to the rectangular potential, we extend the logic to the cases of δ-function and continuous random potentials. We find that the results can be separated in two qualitatively different regimes. In the case where X=FL/E, the results for all different types of potentials considered are qualitatively the same, i.e., the states are localized and lead to a linear correction in the resistance as a function of the current. In the case when X>1, the situation is different: In the δ-function-potential case, and for small values of the field, the states remain localized but with a power-law decay for large L, as found previously. In the rectangular and smooth potential cases considered, we find a transition from localized to extended states as we vary the sample size L. The extended states are unusual in that they have a transmission coefficient which is nonlinear in F for large L. Possible consequences of these results to experiments with wires in metal-oxide-semiconductor field-effect transistors are also discussed.