Substantial Magnetic Fields Arising from Ballistic Ring Currents in Single-molecule Junctions

When a small electric bias is applied to a single- molecule junction, current will flow through the molecule via a tunneling mechanism. In molecules with a cyclic or helical structure there may be circular currents, giving rise to a uni-directional magnetic field. Here, we implement the Biot-Savart law and calculate the magnetic field resulting from the ballistic current density for a selection of molecules. We find that three prerequisites are important for achieving a substantial magnetic field in a single-molecule junction. (1) The current must be high, (2) the ring current must be unidirectional within the bias window, and (3) the diameter of the ring current must be small. We identify both cyclic and linear molecules that potentially fulfill these requirements. In cyclic annulenes with bond-length alternation the current might induce a magnetic field in the mT-range whereas archetypical cyclic molecules, such as benzene, are not suitable candidates for the generation of a substantial magnetic field. Finally, we show that in linear carbon chains with circular current due to their helical π-orbital system, the magnetic field can potentially reach the tesla-range. Our results prove that a large magnetic field can, at least in theory, be induced in molecular wires even at low bias.