EXTENDED STATES IN ONE-DIMENSIONAL LATTICES - APPLICATION TO THE QUASI-PERIODIC COPPER-MEAN CHAIN

The question of the conditions under which one-dimensional systems sup port extended electronic eigenstates is addressed in a very general co ntext. Using real-space renormalization-group arguments we discuss the precise criteria for determining the entire spectrum of extended eige nstates 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 fo r the quasiperiodic copper-mean chain. So far, for the infinite copper -mean chain, only a single energy has been numerically shown to suppor t 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 analyti cally that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.