Aharonov-Bohm interferometry with quantum dots: scattering approach versus tunneling picture

TL;DR

This paper compares two theoretical models for electron transport in Aharonov-Bohm interferometers with quantum dots, establishing their equivalence under certain conditions and analyzing phase effects on transport.

Contribution

It demonstrates the equivalence of tunneling-Hamiltonian and scattering-matrix approaches for modeling quantum dot interferometers and explores phase interplay effects.

Findings

Both models can describe the same experimental setups under specific conditions.

The interplay of Aharonov-Bohm and orbital phases significantly influences transport properties.

The study provides a unified framework for understanding electron transport in quantum dot interferometers.

Abstract

We address the question of how to model electron transport through closed Aharonov-Bohm interferometers which contain quantum dots. By explicitly studying interferometers with one and two quantum dots, we establish the connection between a tunneling-Hamiltonian formulation on the one hand and a scattering-matrix approach on the other hand. We prove that, under certain circumstances, both approaches are equivalent, i.e., both types of models can describe the same experimental setups. Furthermore, we analyze how the interplay of the Aharonov-Bohm phase and the orbital phase associated with the lengths of the interferometers' arms affect transport properties.