How does "Which Way" Detector affect Fano Effect in Mesoscopic Transport --"Phonon-Fano" Or Not

TL;DR

This paper explores how a 'which way' detector influences Fano interference in mesoscopic transport, revealing that the presence or absence of Fano features depends on the modeling approach and system configuration.

Contribution

It compares Markovian and Non-Markovian approaches in double-dot and AB-ring models, clarifying their effects on Fano interference with a 'which way' detector.

Findings

Markovian approach shows no Fano interference at phonon sidebands.

Non-Markovian approach reveals finite Fano interference.

Differences between double-dot and AB-ring models are explained.

Abstract

We investigate the Fano interference in the presence of a "which way" detector, i.e., a local electron-phonon coupler, in the context of mesoscopic transport. Special attention is paid to study whether the phonon sidebands in the differential conductance spectra exhibit the typical lineshape of the Fano interference. When using a double-dot model we obtain two seemly contradictory results by slightly different approaches: The Markovian approach leads to {\it absolutely no} Fano interference at the phonon sidebands, while the Non-Markovian approach results in {\it finite} Fano interference at the phonon sidebands. On the other hand, by using the usual Aharonov-Bohm (AB)-ring model, i.e., only one dot is embedded into one arm of an AB-ring, only the Non-Markovian results are recovered. We explain these contradictory results and make a comparison between the double-dot model and the usual AB-ring model at length. Moreover, we also point out the essential difference between the manifestation of the "which way" effect in mesoscopic double-slit experiments and its optical counterpart.