Aharonov-Bohm oscillations in a mesoscopic ring with asymmetric arm-dependent injection

TL;DR

This paper investigates electron transport and Aharonov-Bohm oscillations in mesoscopic rings with asymmetric arm injection, deriving explicit transmission formulas considering asymmetry and scatterers, extending symmetric ring results to finite-width rings.

Contribution

It introduces a phenomenological parameter for asymmetric injection in mesoscopic rings and derives explicit transmission expressions including scatterer effects.

Findings

Transmission depends on energy, magnetic flux, asymmetry, and scatterer strength.

Results generalize symmetric ring cases and relate to finite-width rings.

Explicit formulas enable analysis of asymmetric electron transport.

Abstract

Electron transport through mesoscopic, one-dimensional rings with asymmetric injection into the arms of the ring is studied, in the presence of a Aharonov-Bohm flux, by means of an appropriate $\boldsymbol{S}$ matrix. This matrix is expressed in terms of two parameters one of which ($\lambda$) accounts phenomenologically for this asymmetric injection into the arms of the ring. In addition, the effect of a scatterer placed in one arm of the ring is considered. Explicit expressions are obtained for the transmission as a function of the incident electron energy, the magnetic field, the asymmetry parameter $\lambda$, and the strength of the scatterer. Results of the literature for symmetric rings are described by $\lambda=1$ and readily recovered. We relate our results to rings of finite width.