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

Abstract

We generalize the quantum waveguide approach to Hückel or tight-binding models relevant to unsaturated $\p$ molecular devices. A Landauer-like formula for the current density through {\em 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.

5 pages, 3 figures

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