Anomalous localisation in the aperiodic Kronig-Penney model

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.