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

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.

Spectral properties of two coupled Fibonacci chains

“…Finally, let us note that the possibility of Bloch-states in coupled aperiodic setups has also been observed in references [12,13], in which more complicated coupling schemes have been used.…”

“…Although the behavior of aperiodic chains has been investigated extensively and in great detail, comparatively little work has been dedicated to the case where two or more chains are coupled to each other, forming an aperiodic ladder [11][12][13][14][15]. In this work, we take a step into this realm by analyzing a range of different coupling schemes between two identical one-dimensional Fibonacci chains.…”

Spectral engineering and tunable thermoelectric behavior in a quasiperiodic ladder network

“…The strength of our analytical attempt lies in the fact that we can obtain an exact mapping of a two or multiarm quasiperiodic ladder network into a set of completely 'isolated' linear chains that describe the quantum mechanics of a class of pseudoparticles. Such an exact mapping has already been demonstrated in ladder-like geometries [16,17,23] modelling a DNA-like double chain or a quasi-two dimensional mesh with correlated disorder in the context of de-localization of single particle eigenstates.…”