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 unidirectional 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-induced magnetic field can approach the mT-range whereas
archetypical cyclic molecules, such as benzene, are not suitable candidates
for the generation of a substantial magnetic field. In linear carbon
chains with circular currents due to their helical π-systems,
the magnetic field is in the mT-range. When the bias window is gated
closer to resonance, we show that the magnetic field can potentially
reach the sub-tesla range. Our results provide proof-of-concept for
achieving experimentally relevant current-induced magnetic fields
in molecular wires at low bias.