When Conductance Is Less than the Sum of Its Parts: Exploring Interference in Multiconnected Molecules

Abstract

We investigate the electron transmission through molecules with multiple connections to the leads and compare this with the transmission through the same molecules where only select connections have been made. This enables us to probe the transmission through the individual pathways through the molecules and investigate their interaction. Generally, we see that the transmission of the multiconnected molecules differs from those obtained from a sum of their parts because of coherence effects between the paths through the molecules. The only exception to this trend is a case where the molecule can be considered as two separate parts, isolated electronically from each other via meta connections. We also explore the local currents though these molecules and separate these into channels, which reveals how this coherence comes into play.

Characterizing destructive quantum interference in electron transport

“…Having developed and described our characterization scheme for DQI, we now apply it to two physical setups that are not well understood. First is DQI at complex energies [11,38,46], and then nontrivial moleculeelectrode couplings [25,33] in the next subsection.…”

“…Our final example looks at systems with nontrivial molecule-electrode couplings [11,25,33]. Most studies of DQI use simple couplings, where each electrode couples to exactly one site of the tight-binding model.…”

“…(Recall that the rank of the self-energy can be loosely interpreted as the number of 'bonds' between the electrode and the molecule.) Hansen and Solomon [33] refer to these couplings as incoherent and coherent, respectively. Such incoherent coupling essentially means that each molecular site independently interacts with the electrode, whereas the two sites' interactions are coordinated in the coherent case.…”

“…These interference vectors possess geometric properties that predict the line shape of the transmission function around DQI, thereby allowing us to characterize DQI.We develop and showcase our analysis of interference vectors through several examples of increasing complexity. Our key findings include a relationship between bound states in a molecular junction and DQI in the same molecule if it were wired to the electrodes in a different configuration, the prediction of so-called supernodes [32] in oligomeric molecules, and the importance of 'coherence' in the molecule-electrode coupling when nontrivial configurations are employed [25,33]. We also apply our analysis to DQI occurring at complex energies, which do not appear to present fundamentally new chemical insights.…”

Constructive quantum interference in a bis-copper six-porphyrin nanoring

“…Quantum interference effects of this type are thought to control electron transfer through proteins123. Quantum interference also provides many opportunities for enhancing performance in single-molecule electronic devices, by creating sharp transport resonances45. When the distance of the transmission exceeds a certain threshold, interactions with vibrational degrees of freedom result in a change of mechanism from phase-coherent single-step tunnelling to incoherent multistep hopping, erasing interference effects67.…”