Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one dimensionality

Abstract

It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side coupled to a suitable subset of sites in the backbone, and if the nearest neighbor hopping integrals, in the backbone and in the side coupled cluster bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone, and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or, a singular continuous one for deterministically disordered lattices) with exponentially (or power law ) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization [P. W. Anderson, Phys. Rev. 109, 1492 (1958)], pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) [Dunlap et al., Phys. Rev. Lett. 65, 88 (1990)].

arXiv comment6 pages, 6 figures, submitted as epl draft

References in corpus (20)

• Fano resonances in nanoscale structures
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Atomic Bose and Anderson glasses in optical lattices
• Fano Resonance in a Quantum Wire with a Side-coupled Quantum Dot
• Multifractal finite-size-scaling and universality at the Anderson transition
• Engineering Fano resonances in discrete networks
• Extended states in 1D lattices: application to quasiperiodic copper-mean chain
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Weak disorder expansion for localization lengths of quasi-1D systems
• Ladder network as a mesoscopic switch: An exact result
• Exponents of the localization lengths in the bipartite Anderson model with off-diagonal disorder
• Localization of Large Polarons in the Disordered Holstein Model
• Controlled engineering of extended states in disordered systems
• Anderson universality in a model of disordered phonons
• Plasmons in disordered nanoparticle chains: Localization and Transport
• Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices
• One-dimensional models of disordered quantum wires: general formalism
• Excitation of coherent polaritons in a two-dimensional atomic lattice
• Measurement-based tailoring of Anderson localization of partially coherent light

Cited by in corpus (6)

• Localization properties and high-fidelity state transfer in electronic hopping models with correlated disorder
• Flux driven and geometry controlled spin filtering for arbitrary spins in aperiodic quantum networks
• Resonant thermoelectric transport in atomic chains with Fano defects
• Complete escape from localization on a hierarchical lattice: A Koch fractal with all states extended
• Engineering insulator-metal transition in a class of decorated aperiodic lattices: a quantum dynamical study
• Engineering complete delocalization of single particle states in a class of one dimensional aperiodic lattices: a quantum dynamical study