The Fano regime of one-dot Aharonov-Bohm interferometers

TL;DR

This paper investigates the mesoscopic Fano effect in Aharonov-Bohm rings with a quantum dot, revealing how magnetic fields influence Fano line shifts and dips through phase control of electron pathways.

Contribution

It demonstrates the magnetic field's role in shifting Fano resonances and explains the periodic movement of Fano dips in terms of phase differences in electron trajectories.

Findings

Fano lines shift with magnetic field due to phase control.

Fano dips move periodically as magnetic field varies.

The effect depends on the ratio of ring to dot area.

Abstract

We use the Landauer-B\"{u}ttiker formalism to study the mesoscopic Fano effect in Aharonov-Bohm rings with an embedded two-dimensional noninteracting dot. The magnetic field dependence of the dot levels leads to a global shift of the Fano lines which becomes important for small ring/dot area ratios. As the magnetic field is varied the Fano dips move periodically from one side of the peak to the other, as reported by Kobayashi {\it et al.} [Phys. Rev. Lett. {\bf 88}, 256806 (2002)]. We show that this effect appears due to a specific magnetic control of the difference between the phase of the single nonresonant path via the free arm of the ring and the global phase of all trajectories involving resonant tunnelings through the dot.