Classifying destructive quantum interference in molecular junctions: Towards molecular quantum rulers

Destructive quantum interference in molecular junctions might be used to build molecular quantum rulers, allowing to quantify changes in external control parameters electrically. For this reason, it is important to understand which patterns of destructive quantum interference can occur inside the electronic excitation gap of a molecule, coupled to conducting electrodes. By considering a four-level model, we show that much more complex destructive quantum interference behavior can arise than expected for just two levels. We classify the destructive quantum interferences analytically and show that they may even occur in regions forbidden by the standard orbital rule for electron transport. Our results suggest that appropriate molecular design may indeed allow to construct highly sensitive molecular quantum rulers.