Controlled delocalization of electronic states in a multi-strand quasiperiodic lattice

TL;DR

This paper demonstrates how tuning hopping parameters in a multi-strand quasiperiodic lattice can control electronic state localization, enabling engineered delocalization and continuous energy spectra in a non-translational system.

Contribution

It introduces a method to engineer extended electronic states in quasiperiodic systems by tuning intra- and inter-strand hopping parameters, revealing controllable delocalization phenomena.

Findings

Energy spectrum exhibits a three-subband self-similar pattern.

Special correlations induce a transition to absolutely continuous spectra.

Extended Bloch-like states can be engineered through parameter tuning.

Abstract

Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of such a multi-strand quasiperiodic network is found to be sensitive on the mutual values of the intra-strand and inter-strand tunnel hoppings, whose distribution displays a unique three-subband self-similar pattern in a parameter subspace. In addition, it is observed that special numerical correlations between the nearest and the next-nearest neighbor hopping integrals can render a substantial part of the energy spectrum absolutely continuous. Extended, Bloch like functions populate the above continuous zones, signalling a complete delocalization of single particle states even in such a non-translationally invariant system, and more importantly, a phenomenon that can be engineered by tuning the relative strengths of the hopping parameters. A commutation relation between the potential and the hopping matrices enables us to work out the precise correlation which helps to engineer the extended eigenfunctions and determine the band positions at will.