A renormalization group analysis of extended electronic states in 1d quasiperiodic lattices

Details A renormalization group analysis of extended electronic states in 1d quasiperiodic lattices A renormalization group analysis of extended electronic states in 1d quasiperiodic lattices

1994-07-07

arxiv.org/abs/cond-mat/9407038v1

Physics

Condensed Matter

19 pages, 7 figures available on request, LaTeX version 2.09, SINP-AKRS94-01

Scientific paper

10.1103/PhysRevB.50.13276

We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasi-periodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. {\bf 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 quasi-periodic period-doubling chain, whose spectrum is found to exhibit a rich variety of behaviour, including a cross-over 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 non-vanishing. Results are presented for different parameter regimes, yielding both periodic as well as non-periodic eigenfunctions. We have also extended the present theory to a multi-band model arising from a quasi-periodically arranged array of $\delta$-function potentials on the atomic sites. Finally, we present a multifractal analysis of these wavefunctions following the method of Godreche and Luck [ C. Godreche and J. M. Luck, J. Phys. A :Math. Gen. {\bf 23},

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