Magnetic fields effects on the electronic conduction properties of molecular ring structures

While mesoscopic conducting loops are sensitive to external magnetic fields, as is pronouncedly exemplified by observations of the Aharonov-Bohm (AB) effect in such structures, the small radius of molecular rings implies that the field needed to observe the AB periodicity is unrealistically large. In this paper, we study the effect of magnetic field on electronic transport in molecular conduction junctions involving ring molecules, aiming to identify conditions where magnetic field dependence can be realistically observed. We consider electronic conduction of molecular ring structures modeled both within the tight-binding (Hückel) model and as continuous rings. We also show that much of the qualitative behavior of conduction in these models can be rationalized in terms of a much simpler junction model based on a two-state molecular bridge. Dephasing in these models is affected by two common tools: the Büttiker probe method and coherence damping within a density matrix formulation. We show that current through a benzene ring can be controlled by moderate fields provided that several conditions are satisfied: (a) conduction must be dominated by degenerate (in the free molecule) molecular electronic resonances, associated with multiple pathways as is often the case with ring molecules, (b) molecular-leads electronic coupling must be weak so as to affect relatively distinct conduction resonances, (c) molecular binding to the leads must be asymmetric (e.g., for benzene, connection in the meta or ortho, but not para, configurations), and (d) dephasing has to be small. When these conditions are satisfied, considerable sensitivity to an imposed magnetic field normal to the molecular ring plane is found in benzene and other aromatic molecules. Interestingly, in symmetric junctions (e.g., para-connected benzene), the transmission coefficient can show sensitivity to magnetic field that is not reflected in the current-voltage characteristic. The analog of this behavior is also found in the continuous ring and the two-level models. Although sensitivity to magnetic field is suppressed by dephasing, quantitative estimates indicate that magnetic field control can be observed in suitable molecular conduction junctions.