Universal Scaling of Electron Transmission for Nearly Ballistic and Quantum Dragon Nanodevices

Abstract

We predict two different universal scaling regimes for the quantum transmission of metallic nanodevices following the addition of a small amount of uncorrelated disorder. A nanodevice is connected to two thin semi-infinite uniform leads, and the Non-Equilibrium Green's Function (NEGF) methodology yields the electron transmission $\mathcal{T}(E)$ as a function of the injected electron energy $E$. Ballistic nanodevices have no disorder and have $\mathcal{T}(E)=1$ for all $E$ that allow electron propagation in the leads. Quantum dragon nanodevices can have extremely strong properly correlated disorder, and still have $\mathcal{T}(E)=1$ for all $E$. Additional uncorrelated site disorder leads to Fano resonances in $\mathcal{T}(E)$. Averaging over the uncorrelated disorder we predict using perturbation theory two universal scaling regimes for ${\mathcal{T}}_{\mathrm{ave}}(E)$. The functional form of both universal scaling regimes depend on the device length and width, energy, and variance of the uncorrelated disorder. The second scaling regime, valid for small but somewhat larger uncorrelated disorder than the first scaling regime, also has the form dependent on the density of states of the system. These two scaling regimes are demonstrated to be valid via large scale computer calculations.

V2: 25 pages, 10 figures; the message from V1 remains the same. However, V1 has been split into three papers. Version 2 is the 2025 publication in "Chaos, Solitons & Fractals" for universal scaling near ballistic or quantum dragon nanodevices. The 'Order amidst Disorder' calculations are published in Journal of Physics: Conference Series 1740(2021) 012002 and Europhys. Lett. 143, 26005 (2023)