Theory of transmittance of narrow quantum wires intersection in 2D systems

TL;DR

This paper models the transmittance of narrow quantum wire intersections in 2D systems using conformal mappings, providing analytical solutions for T-like and X-like crossings.

Contribution

It introduces a simplified Schrödinger equation approach for tunnel conductors and derives transmittance formulas for specific wire intersection geometries.

Findings

Transmittance formulas for T-like and X-like wire crossings are obtained.

The Schrödinger equation reduces to Laplace's equation under the tunnel conductor assumption.

Analytical solutions are derived using conformal mapping techniques.

Abstract

The transmittance of intersection between narrow quantum strips is studied. It is assumed that strip widths are less than the electron wavelength, so that they are tunnel conductors. In this assumption the Schr\"odinger equation is reduced to the Laplace one, which can be solved by the conformal mappings. The transmittances of T-like and X-like wire crossings are found.