How ubiquitous are dragon segments in quantum transmission?

TL;DR

This paper investigates the conditions under which nanodevices modeled as weighted graphs can achieve perfect electron transmission, introducing methods to tune these graphs into quantum dragons with energy-independent transmission.

Contribution

It provides theoretical proofs and three practical prescriptions for tuning weighted graphs into quantum dragons, enabling perfect transmission in nanodevices.

Findings

Any nanodevice can be tuned into a quantum dragon with proper parameter adjustment.

Three specific prescriptions are proposed for tuning weighted graphs into quantum dragons.

The implications for physical nanodevices are discussed.

Abstract

Quantum dragon segments are nanodevices that have energy-independent total transmission of electrons. At the level of the single-band tight-binding model a nanodevice is viewed as a weighted undirected graph, with a vertex weight given by the on-site energy and the edge weight given by the tight-binding hopping parameter. A quantum dragon is a weighted undirected graph which when connected to idealized semi-infinite input and output leads, has the electron transmission probability ${\cal T}(E)$$=$$1$ for all electron energies $E$. The probability ${\cal T}(E)$ is obtained from the solution of the time-independent Schr\"odinger equation. A graph must have finely tuned tight-binding parameters in order to have ${\cal T}(E)$$=$$1$. This paper addresses classes of weighted graphs which can be tuned, by adjusting a small fraction of the total weights, to be a quantum dragon. We prove that with proper tuning any nanodevice can be a quantum dragon. Three prescriptions are presented to tune a weighted graph into a quantum dragon nanodevice. The implications of the prescriptions for physical nanodevices is discussed.