Universal Scaling for Electron Transmission in Nearly Ballistic And Quantum Dragon Nanodevices

The electrical conductance is proportional to the electron transmission probability T(E_F) at the Fermi energy E_F when a nanodevice is connected to a source and sink of electrons via long leads. We study via a tight-binding model two types of devices that have T(E)=1 for all energies that propagate through the attached leads. Ballistic nanodevices have no disorder, and using Bloch wavefunction analysis, have T(E)=1. A quantum dragon nanodevice [1] has arbitrarily strong correlated disorder but still has T(E)=1. Adding uncorrelated random site disorder to models for quantum dragon or for ballistic nanodevices one can calculate a transmission T_ave(E) that averages over the Fano resonances in T(E). Using NEGF (NonEquilbrium Green's Function) methods, we obtain universal scaling forT_ave(E) in two different scaling regimes. The scaling is tested for pure and disordered graphene and single-walled carbon nanotubes, and for numerous quantum dragon nanodevices. We show the scaling works extremely well for any nearly ballistic or nearly quantum dragon nanodevice.
[1] M.A. Novotny, PRB 90, 165103 (2014).
[2] M.A. Novotny and T. Novotný, Order amidst Disorder in semi-regular, tatty, and atypical random nanodevices with locally correlated disorder, arXiv:2007.01051