Generalized waveguide approach to tight-binding wires: understanding large vortex currents in quantum rings

We generalize the quantum waveguide approach to Hückel or tight-binding models relevant to unsaturated π molecular devices. A Landauer-type formula for the current density through internal bonds is also derived which allows for defining a local conductance. The approach is employed to study internal circular currents in two-terminal rings. We show how to predict the occurrence and the nature of large vortex currents in coincidence with vanishingly small currents in the leads. We also prove a remarkably simple formula for the onset of a vortex regime.