Renormalization-group analysis of extended electronic states in one-dimensional quasiperiodic lattices

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Abstract
We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasiperiodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. B 48, 4192 (1993)], within the framework of the real-space renormalization-group approach. It is shown that even in the absence of translational invariance, extended states arise in a class of such lattices if they possess a certain local correlation among the constituent atoms. We have applied these ideas to the quasiperiodic period-doubling chain, whose spectrum is found to exhibit a rich variety of behavior, including a crossover from critical to an extended regime, as a function of the Hamiltonian parameters. Contrary to prevailing ideas, the period-doubling lattice is shown to support an infinity of extended states, even though the polynomial invariant associated with the trace map is nonvanishing. Results are presented for different parameter regimes, yielding both periodic as well as nonperiodic eigenfunctions. We have also extended the present theory to a multiband model arising from a quasiperiodically arranged array of δ-function potentials on the atomic sites. Finally, we present a multifractal analysis of these wave functions following the method of Godreche and Luck [J. Phys. A 23, 3769 (1990)] to confirm their extended character.
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