Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices

TL;DR

This paper demonstrates that in certain disordered and quasiperiodic lattices, electronic states can be entirely extended and delocalized by tuning local or non-local couplings, challenging conventional localization expectations.

Contribution

The study provides exact analytical conditions for achieving extended electronic states in disordered and quasiperiodic systems through specific coupling controls and magnetic fields.

Findings

Entire energy spectrum can be absolutely continuous with extended states.

Delocalization depends on fine-tuned Hamiltonian parameter correlations.

Results are supported by analytical derivations and numerical simulations.

Abstract

We show that a discrete tight-binding model representing either a random or a quasiperiodic array of bonds, can have the entire energy spectrum or a substantial part of it absolutely continuous, populated by extended eigenfunctions only, when atomic sites are coupled to the lattice locally, or non-locally from one side. The event can be fine-tuned by controlling only the host-adatom coupling in one case, while in two other cases cited here an additional external magnetic field is necessary. The delocalization of electronic states for the group of systems presented here is sensitive to a subtle correlation between the numerical values of the Hamiltonian parameters - a fact that is not common in the conventional cases of Anderson localization. Our results are analytically exact, and supported by numerical evaluation of the density of states and electronic transmission coefficient.