Anomalous localisation near the band centre in the 1D Anderson model: Hamiltonian map approach

• Published in: Physica. E, Low-dimensional systems & nanostructures Vol. 44; no. 7-8; pp. 1260 - 1266
• Main Authors: Tessieri, L., Herrera-González, I.F., Izrailev, F.M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2012; Elsevier
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Electronic structure of nanoscale materials : clusters, nanoparticles, nanotubes, and nanocrystals; Exact sciences and technology; Physics; Electronic structure; Anderson model; Analytical solution; Hamiltonians; Scaling laws; One dimensional model
• ISSN: 1386-9477; 1873-1759
• DOI: 10.1016/j.physe.2012.01.024

We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns out to be more effective than other known methods. The analytical expressions are supported by numerical data. We also discuss the implications of our results for the single-parameter scaling hypothesis. ► Focus: the band-centre anomaly in the 1D Anderson model with diagonal disorder. ► Result: analytical expression of the localisation length close to the band centre. ► Remark: extension of the Derrida–Gardner formula beyond the exact band centre. ► Discussion: implications for the validity of the single-parameter scaling hypothesis.