Localization-delocalization in aperiodic systems
2002 (English)In: Physical Review B, Condensed matter and materials physics, ISSN 1098-0121 (print) 1550-235x (online), Vol. 66, no 9, 094204- p.Article in journal (Refereed) Published
The question of localization in a one-dimensional tight-binding model with aperiodicity given by substitutions is discussed. Since the localization properties of the well-known Rudin-Shapiro chain is still far from well understood, partly due to the absence of rigorous analytical results, we introduce a sequence that has several features in common with the Rudin-Shapiro sequence. We derive a trace map for this system and prove analytically that the electron spectrum is singular continuous. Despite the extended (non-normalizable) nature of the corresponding wave functions, the states show strong localization for finite approximations of the chain. Similar localization properties are found for the Rudin-Shapiro chain, where earlier results have indicated a pure point spectrum. We compare the properties for two other physical systems, ordered according to the two discussed sequences; stationary electron transmission is studied through finite chains using a dynamical map, optical properties of dielectric multilayer structures are investigated.
Place, publisher, year, edition, pages
2002. Vol. 66, no 9, 094204- p.
IdentifiersURN: urn:nbn:se:liu:diva-14650DOI: 10.1103/PhysRevB.66.094204OAI: oai:DiVA.org:liu-14650DiVA: diva2:24114