Current vortices in aromatic carbon molecules

The local current flow through three small aromatic carbon molecules, namely, benzene, naphthalene, and anthracene, is studied. Applying density functional theory and the nonequilibrium Green's function method for transport, we demonstrate that pronounced current vortices exist at certain electron energies for these molecules. The intensity of these circular currents, which appear not only at the antiresonances of the transmission but also in the vicinity of its maxima, can exceed the total current flowing through the molecular junction and generate considerable magnetic fields. The $\ensuremath{\pi}$ electron system of the molecular junctions is emulated experimentally by a network of macroscopic microwave resonators. The local current flows in these experiments confirm the existence of current vortices as a robust property of ring structures. The circular currents can be understood in terms of a simple nearest-neighbor tight-binding H\"uckel model. Current vortices are caused by the interplay of the complex eigenstates of the open system which have energies close to the considered electron energy. Degeneracies, as observed in benzene and anthracene, can thus generate strong circular currents, but also nondegenerate systems like naphthalene exhibit current vortices. Small imperfections and perturbations can couple otherwise uncoupled states and induce circular currents.