Extended states in one-dimensional lattices: Application to the quasiperiodic copper-mean chain

Abstract

The question of the conditions under which one-dimensional systems support extended electronic eigenstates is addressed in a very general context. Using real-space renormalization-group arguements we discuss the precise criteria for determining the entire spectrum of extended eigenstates and the corresponding eigenfunctions in disordered as well as quasiperiodic systems. For purposes of illustration we calculate a few selected eigenvalues and the corresponding extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for the infinite copper-mean chain, only a single energy has been numerically shown to support an extended eigenstate [J. Q. You, J. R. Yan, T. Xie, X. Zeng, and J. X. Zhong, J. Phys.: Condens. Matter 3, 7255 (1991)]: we show analytically that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.