Anomalous localisation in the aperiodic Kronig-Penney model

TL;DR

This paper investigates the unusual localization properties of electronic states in a disordered Kronig-Penney model, revealing resonant effects and anomalous scaling near band edges and centers, similar to Anderson localization phenomena.

Contribution

It demonstrates the presence of anomalous localization effects and the impact of cross-correlations in disorder, extending understanding of electronic states in aperiodic systems.

Findings

Localization length shows resonant effects near the band center.

Anomalous scaling occurs at the band edges.

Cross-correlations can induce highly localized states.

Abstract

We analyse the anomalous properties of specific electronic states in the Kronig-Penney model with weak compositional and structural disorder. Using the Hamiltonian map approach, we show that the localisation length of the electronic states exhibits a resonant effect close to the band centre and anomalous scaling at the band edges. These anomalies are akin to the corresponding ones found in the Anderson model with diagonal disorder. We also discuss how specific cross-correlations between compositional and structural disorder can generate an anomalously localised state near the middle of the energy band. The tails of this state decay with the same stretched-exponential law which characterises the band-centre state in the Anderson model with purely off-diagonal disorder.