Delocalization in Continuous Disordered Systems

TL;DR

This paper investigates how specific statistical correlations in continuous one-dimensional disordered systems can lead to delocalized states, challenging traditional localization theories and providing insights into conductance behavior.

Contribution

It demonstrates that correlations in disordered potentials can induce extended states and analyzes their critical properties and conductance implications.

Findings

Delocalized states occur at specific energies due to correlation rules.

Critical exponent of 2/3 for localization length divergence in delta-barrier models.

Vanishing transmission fluctuations at peak conductance.

Abstract

Continuous One-dimensional models supporting extended states are studied. These delocalized statesoccur at well defined values of the energy and are consequences of simple statistical correlation rules. We explicitly study alloys of delta-barrier potentials as well as alloys and liquids of quantum well as.The divergence of the localization length is studied and a critical exponent 2/3 is found for the delta-barrier case, whereas for the quantum wells we find an exponent of 2 or 2/3 depending on the well's parameters. These results support the idea that correlations between random scattering sequences break Anderson localization. We further calculate the conductance of disordered superlattices. At the peak transmission the relative fluctuations of the transmission coefficient are vanishing.