Order amidst disorder in semi-regular, tatty, and atypical random nanodevices with locally correlated disorder

Abstract

We make unexpected predictions for the electrical conductance and local density of states (LDOS) of a wide class of semi-regular nanodevices, tatty nanodevices, and nanodevices with atypical but arbitrarily strong disorder. Disorder is disruptive to electron transport, as it causes coherent electron scattering. Nevertheless, we predict a wide class of nanodevices which show order amidst disorder, in that the device Hamiltonians are disordered but when the device is attached to proper leads the LDOS is ordered. These nanodevices also are quantum dragons, as they have complete electron transmission, T (E) = 1 for all electron energies which propagate in the attached leads. We analyze a conventional single-band tight-binding model by NEGF (Non-Equilibrium Green's Function) methods. We provide a recipe to allow extensive disorder in coherent transport through quantum nanodevices based on semi-regular, random, or tatty 2D, 3D, and 2D+3D underlying graphs with arbitrarily strong disorder in the tight-binding parameters, while the nanodevice keeps the desired quantum properties. The tight-binding parameters must be locally correlated to achieve order amidst disorder and T (E) = 1. Consequently, in addition to the known regular examples of armchair single-walled carbon nanotubes and zigzag graphene nanoribbons, we predict a large class of metallic allotropes of carbon with T (E) = 1. We also provide in two different regimes universal scaling analysis for the average transmission, Tave(E), for nanodevices which have nearly the desired quantum properties.