The Effect of Fano Resonance on ExchangeInteraction in a DQD Junction with RashbaSpin-Orbit Coupling

In this work, we investigate electronic transport through a double quantum dot junction, where each dot couple to external localized spins. The junction is embedded in between two metallic leads,functioning as continues electron reservoirs. The double quantum dotjunction forms in the junction a bonding and anti-bonding state, muchresembling the electronic structure of a molecule, hence provides in-sight to such systems. Due to the nature of the parallel coupling weexpect a reduced tunneling through the anti-bonding state as a resultof destructive interference as the tunneling is provided multiple path-ways through the molecule. We predict that signature effects arisecorrelating the quantum observable to the effective exchange couplingbetween the localized spin moment and the electronic structure of theDQD. We expect the Fano resonance to disappear entirely when the anti-bonding state is localized and the transmission is carried purely through the bonding state. We further investigate the effects of in-clusion of Rashba Spin-Orbit coupling, allowing decoherence in thetransport. Here, a further degree of freedom is available and morecontrol of the quantum interference and hence the signatures in theexchange is allowed