Quantum Dragon Solutions for the Tight Binding Model of 2D Ribbon Nanodevices.

We present quantum dragon solutions for electron transport for the tight binding model with strong disorder in nanoribbons based on 2D hexagonal, rectangular, and square-octagonal graphs. When the nanodevice is connected between two thin semi-infinite leads, the Landauer formula gives the electrical conductance, $ G $. The electron transmission probability, ${\cal T}(E)$ from the solution of the time-independent Schr{\"o}dinger equation, yields $ G=\big(2e^2/h\big){\cal T}(E)$. In the presence of uncorrelated randomness, $ {\cal T}(E)\ll 1 $ for most electron energies, $ E $. Recently, the theoretical discovery of a large class of nanostructures called quantum dragons has been published [1]. Quantum dragon nanodevices have strong, correlated randomness but have ${\cal T}(E)=1$ for all $ E $ of electrons which propagate through the leads. Here, we show that both uniform leads and dimerized leads coupled to hexagonal, rectangular, and square-octagonal graphs with different boundary conditions can have the quantum dragon property [2]. We discuss how added disorder affects ${\cal T}(E)$ near a quantum dragon solution, and discuss experiments relevant to quantum dragon nanodevices.
[1] M.A. Novotny, Phys.Rev B, 2014
[2] G. Inkoom, Ph.D., Dissertation, Mississippi State University, 2017.