Power-law localization at the metal-insulator transition by a quasiperiodic potential in one dimension

Abstract

The localization properties of an electron in the tight-binding potential \ensuremath{\lambda} cos(\ensuremath{\pi}\ensuremath{\alpha}${\mathit{n}}^{\ensuremath{\nu}}$), where 01, are investigated. Wave functions approaching the metal-insulator transition (MIT) ${\ensuremath{\lambda}}_{\mathit{c}}$=2-\ensuremath{\Vert}E\ensuremath{\Vert} (or the mobility edges ${\mathit{E}}_{\mathit{c}}$=\ifmmode\pm\else\textpm\fi{}\ensuremath{\Vert}2-\ensuremath{\lambda}\ensuremath{\Vert}) from the metallic region are found to localize with multiple well-separated power-law decaying peaks, contradicting previous conclusions obtained with the help of the Lyapunov exponent. The general expectation of exponential localization with divergent localization length at the MIT cannot be detected convincingly.