Self-similarity of single-channel transmission for electron transport in nanowires

TL;DR

This paper reveals that single-channel electron transmission in nanowires shows self-similarity across length and energy, enabling the prediction of transmission properties through nonlinear transformations.

Contribution

It introduces a novel concept of self-similarity in electron transmission, allowing for the design of transformations to predict transmission in different regimes based on known data.

Findings

Self-similarity observed in resonance tunneling transmission.

Transformations enable prediction of transmission for various lengths and energies.

Density functional theory confirms self-similarity in Na atomic wires.

Abstract

We demonstrate that the single-channel transmission in the resonance tunneling regime exhibits self-similarity as a function of the nanowire length and the energy of incident electrons. The self-similarity is used to design the nonlinear transformation of the nanowire length and energy which, on the basis of known values of transmission for a certain region on the energy-length plane, yields transmissions for other regions on this plane. Test calculations with a one-dimensional tight-binding model illustrate the described transformations. Density function theory based transport calculations of Na atomic wires confirm the existence of the self-similarity in the transmission.